First, never assume that the foreign grammar will be just like English grammar. Most languages have genders assigned to nouns and agreement rules for adjectives that do not exist in English. Word order might be completely the opposite, and certain verb tenses might be used in different situations. Some languages never use articles, while other use them almost all the time. You might have to learn what cases and declensions are, or how to conjugate verbs in the perfective and imperfective aspects. Even punctuation could be different than what you're used to. But the most basic topics of grammar, like nouns or prepositions, exist in all languages and are used the same way by definition. (i.e. a noun will always be a person, place, thing or idea no matter what language the word is in.)
When learning a new language, it is necessary to use the language everyday and study whenever you possibly can. For learning vocabulary, you could start by writing your "to do" lists in the language, or even giving commands to your dog. Label household items, like the table or television, with the word in the language and start translating everything you see or read or hear into the new language. See how fast you can switch between the two (or more) languages in your mind.
► Reading & Writing
Reading a foreign language is usually the easiest aspect of learning. Unless you are learning a language that uses a different alphabet than your native language; in that case, speaking might be the easiest. Anyway, you can find lots of newspapers online in virtually every language, and many sites have language options, such as Yahoo. Some government websites have bilingual pages, such as those of Canada and Switzerland. Reading blogs, newsgroups or forums is a great way to learn slang and colloquialisms. You can also try reading some children's book to begin with, then moving up to regular novels. You might have problems finding foreign language materials at your library, but most bookstores have at least a few children's books in different languages. Project Gutenberg contains thousands of books (in several languages) online that you can download for free. Dual language books are also a great resource and can be purchased from Dover Publications at very cheap prices. I highly recommend using readers and translating as much as possible when you begin studying a language. Becoming familiar with certain expressions and ways of writing is very helpful with vocabulary acquisition and certain nuances of the language, such as idioms and proverbs.
E-mail pen pals is an option for writing and also learning about the little aspects of culture. There isn't much else you can do for writing unless you have a teacher who can correct your mistakes. That's why I study grammar so rigorously; I try to become perfect so that I won't need any corrections on my writing. You can try some online translating services if you need a quick translation, but don't count on them to have perfect grammar or even the correct translations of some words. There are also some online dictionaries for a lot of languages, such as WordReference (for French, Italian, Spanish, German & Russian) and LEO for German.
Some books you need to buy are a dictionary (preferably one with pronunciations for every word); a book of verb conjugations; and a grammar review. If you can find a dictionary with complete verb conjugations, then you can get by with only that one book because you can find almost all grammar online. Books of vocabulary may be helpful for quick reference, but I think it's more wise to get a cassette or CD of vocabulary so you know exactly how the words sound, such as Vocabulearn. However, for languages such as French, which slur most of the words together in a sentence, learning just the words might not help much. In this case, it would be better to listen to whole sentences.
► Problems with Language Books
One problem with foreign language books is that the majority of them cater to the traveler who just wants to get by in the language and not actually speak it fluently. Another problem is that most books do not present the grammar in an order conducive to learning or even in an order that corresponds to the frequency of usage in the language. This is the major problem I see with high school and college textbooks. For example, the past tense of verbs is not even introduced until about the 6th chapter, so the student must speak only in the present tense for weeks or months! In addition, the sample sentences given in those books are so boring and pointless because native speakers rarely use them. If the books included more colloquialisms or slang words, as well as certain fixed expressions that are vital for survival in the language, then maybe more students would be interested in taking foreign language classes in school. But as long as school curricula continue to focus solely on form and not meaning, then students will only learn how to conjugate verbs or decline nouns, but never be able to actually speak the language.
Nevertheless, there are some books that are rather helpful for learning languages. You can find some cheap books on Ebay, although I would advise to actually look at the book first before buying it online. In my experience, books by Dover Publications and the NTC publishing company (now part of McGraw-Hill) are the least expensive and most useful, especially if you're looking for vocabulary books or short stories. I also love Living Languages (part of Random House) full language courses. Living Language's Ultimate Series is available in French, German, Italian, Spanish, Portuguese, Russian, Japanese and Chinese. The books are equivalent to two years of college level study, and there are also 8 hours of recordings, but you have to buy those separately. For dictionaries and grammar books, I recommend the Routledge series because they are so comprehensive. The dictionaries include the pronunciation of every word, plus plural forms of nouns and other pertinent information that most dictionaries tend to ignore. And the grammar books are available for a wide range of languages; however, the only drawback is that most cost around $30 USD.
You can visit my Amazon store for books that I recommend in French, Spanish, Italian and German.
► Listening & Speaking
Listen to the language as much as possible. Listening is the best way to improve your pronunciation in addition to comprehension. This will probably be your weakest point, especially if you live in a country that has little access to foreign languages. There are many, many podcasts and radio stations available through iTunes or Realplayer or through their own websites, or just switch the spoken language feature to French or Spanish on the DVDs you already own. Don't rely on the subtitles to exactly match what is spoken though. The translations are more cultural than literal.
Yabla is perhaps the best language learning tool I have found online and it is not very expensive. It is online video immersion using real, authentic language. Subtitles and translations into English are provided on screen, and you can slow down the playback if needed. Currently it is available in French, Spanish and German.
As for podcasts, the Praxis language Pods are high quality and available in French, Spanish, Italian and Chinese.
If you just need the pronunciation of one word, try Forvo.
► Audio-Visual Programs
BBC Languages is a great site with free audio and video files. The Muzzy video program is designed for children and is available in French, Spanish, Italian, and German; but I'm sure adults can profit from it too. The Victor Ebner series is an immersion video method for learning French, Italian, Spanish, German and even Swiss German. French in Action, Destinos and Fokus Deutsch are three great video programs for French, Spanish and German.
I have used the French in Action videos and cassettes in my college classes, and I highly recommend them, though they are quite dated now. Most college libraries have the videos, but I doubt local libraries would. Every once in a while the tapes and textbooks are sold on Ebay, so I would suggest trying there first before spending $400 on them from the publishing company. Better yet, the company that produces the programs, the Annenberg/CPB project, has all of the videos on their website that you can watch if you have a broadband connection (but only if you are in the US or Canada). You have to sign up on the website, but it's free and some of the transcripts are also available online so you can read along with the dialog.
► Slang & Informal Language
If you can find the scripts for the movies and televisions shows (try allsubs.org), then you can read along with the audio. This is a great way to learn slang and idioms. There are some books written exclusively for slang, such as the Slangman/Street series or the Streetwise series in French, Italian, Spanish and German. CDs or cassettes are available to use with the books. Tune up Your French and Tune up your Spanish are also available from McGraw-Hill, and a CD is included. Bertlitz's website has many downloadable audio files to go with the books. The Hide this Book series is written specifically for slang.
If you can afford to spend a little money, you can get some tapes or CDs of vocabulary or even CD-Roms that let you speak into a microphone to judge how well you sound like a native speaker. There are a lot of tapes that go with phrase books too that might be useful. The tapes that I would definitely recommend are of verb conjugations. Living Language makes some cassettes called "A Conversational Approach to Verbs" which includes pronunciations of all the verb tenses. This is very helpful since most other cassettes only include the present tense of verbs. You can check on Ebay or half.com for these tapes too, so you don't have to pay full price. Or you could try outlet book stores, such as Borders Outlet.
Listening to songs in the target language also helps with increasing vocabulary since rhymes are more easily remembered, and you can usually find the lyrics online. The site Lyrics Training is great for this.
Using the internet is the best way to expose yourself to authentic language. You should try reading blogs and forums in addition to the news so that you will understand both informal and formal language. Blogger, Livejournal, Wordpress and Typepad are all blogging sites, mostly in English but you can find blogs written in other languages, and over-blog is mostly in French. You can use search engines as a way to check your grammar, especially if you aren't sure of the word order or if a preposition follows the verb. Just type your phrase into the search box and see if anyone else has used the same sentence or to see what other similar phrases may exist. Also try Google Battle to see which phrase is used more often... though this doesn't necessarily mean it is correct!
► Radio & TV
Many radio stations all over the world let you listen to their programs for free online. Even if you don't understand everything, you will still be exposing yourself to the intonation and stress of the language, which is extremely important for learning proper pronunciation. Many television stations provide clips from their news programs, such as France2. TV channel sites also provide a lot of cultural information about the country that is the most up-to-date.
Before You Know It (by Transparent Language) is a great flash card program that you can download for free to study words and phrases in several languages (with audio, of course). The language courses written for the Foreign Service Institute are in the public domain and most of the texts and audio files can be downloaded for free at the FSI Language Courses site. However, as there are no copyright restrictions on these materials, this means that publishing companies can copy the books and audio files and sell them for profit. Unless you absolutely cannot find the materials online or in a library, I would advise against buying FSI courses through online bookstores. (In addition, I am turning some of the FSI courses into HTML versions.)
I cannot stress enough how important the exposure to real, authentic language is! Do not rely solely on books because they contain constructed sentences that are not taken from real life. The internet is your best source of information on informal language and the way that people really speak (and write), which do not follow the grammatical rules you learn from books. There is an amazing range of language learning opportunities online, and not only from websites and podcasts. The internet may be your only option for learning authentic language and seeing the real culture of the countries that speak it, especially if you have never have the chance to visit those countries. My Realia section currently contains authentic objects, such as train tickets, brochures, menus, etc. so you can see the language as it is actually used.
Remember: The focus of your language studies should be more on meaning (words and phrases) and less on form (grammatical rules).