There are various ways of learning Lojban unique to the individual learning it, but to help you get started here are some suggestions.
To get started with the general structure of the Lojban language you will need to begin reading one or more of the Lojban books, such as the freely available online The Complete Lojban Language and What is Lojban?. These books will teach you about how to read and use Lojban; what the different types of words and grammatical constructs do, how to use them and interpret them; how to express yourself Lojbanically. They will not, however, teach you vocabulary, style, spoken flow, nor other aspects involved in really learning about and using a human language.
The Lojban books teach you how to use Lojban, but they don't help you learn the whole vocabulary. For that you will need word lists, and flashcard sets such as Quizlet (it's online; register and join the lojban group), jMemorize (downloadable) or Logflash (if you are more technically inclined and like MS-DOS). Also, take a look at the jbovlaste dictionary. You will need to have read a little, from one of the learning texts, about Lojban to know what kind of words you need to learn.
A set of pronunciation guides are available to help you speak Lojban.
Try reading a progression of proofread (proofed by at least one lojbanist in addition to the author) lojban texts, starting with short-and-easy through to long-and-difficult. For example, read Terry the Tiger (you can listen to this one too!), then The Berenstain Bears and the Prize Pumpkin, then The Little Prince. For conversational text, try Everyday Lojban.
The two most active points of communication for the Lojban community are the Lojban mailing list and the Lojban IRC chat room. Depending on your preferences, one or both of these will meet your needs. For those unfamiliar with mailing lists, there is a web forum interface to it, which some prefer. There is also a Lojban LiveJournal community, and the Lojban MOO, that is, a multi user virtual environment, kind of like the old text adventure games.
A good idea is to familiarise yourself with common expressions such as Lojban greetings to get you started in chatting Lojban with other Lojbanists. The Lojban IRC cheat sheet provides some useful fundamental vocabulary.
Start memorizing the vocabulary and using Lojban as much as you can! Chatting with the community can help you with this. Writing a personal diary or performing translations, are other possibilities. Lojban means different things to different people; for some it is a linguistic curiousity — a test-bed for language experimentation; for others a way to expand their mind or discipline their thought; the desire for precise expression; a new way to look at languages; a fun way to meet and communicate with friends; entertainment; a challenge; art; software application; the list goes on! What will Lojban mean for you?
Once you know what words you want to learn, you could try memorization software to vastly improve your vocabulary. Chatting regularly on the Lojban IRC channel is another way of using your vocabulary in real time. Some start blogs or diaries, others translate music.