Do not underestimate reading. Read in the language as much as you can. Try children's stories first, moving on to newspapers and magazines as your vocabulary builds. Reading will dramatically improve your vocabulary, your spelling, your grammar and your knowledge of the language culture. It is almost a prerequisite for good writing.
Get yourself bilingual books. Or get a book in the new language and the same book in one you already know. Read them together, matching words in the two languages. It helps if the languages are quite close. For instance, learning Spanish is easier starting from French than from English, because it's easier to see the more general structures.
Relating to the above, one could watch a favorite film with audio in one language and subtitles of another. Anime fans will be pretty familiar with this method.
A very good "first read" is the book "The Little Prince" by Antoine de Saint-Exupéry. Originally in French, it is easily available in a lot of different languages. In many languages, it is even online (legally), and can be read for free. The book is short, interesting (even philosophical) and contains simple grammar and vocabulary. Another good book, for similar reasons, is "The Wonderful Wizard of Oz" by L. Frank Baum.
Speed reading doesn't help when beginning to learn a language. Lip read so that you can hear yourself speaking. Speed reading discourages vocalization which is important when starting to learn a language. Speed reading of course has its place, but while beginning a language, a lot of 'hard' reading is required. Fundamental words and sentences need to be mastered. When one feels confident enough or is at an intermediate level, speed reading may help or could even be recommended.
Get a digital dictionary. The much speedier word look-up will greatly ease your first readings. Plus, the clear separation of word meanings (which most paper dictionaries can't afford) will make it easier to grasp new words. Freedict offers a collection of freely available (and modifiable) dictionaries.
Once you get a sufficient level of writing you can try to write on Wikimedia projects. You could try to add (or start) a Wikibook for learning a language, or translate a Wikipedia article of your interest, knowing that others, more advanced or native speakers, will correct you!