Learn the Thai alphabet. Like Chinese, Thai is a tonal language, but unlike Chinese, there is a relatively small alphabet to learn. It's much larger than English, however, and besides letters, you will have to learn tone indicators. Print a chart of the entire Thai alphabet, with tones. Omniglot has a handy Thai alphabet page which includes all of these.
Practice your pronunciation. You not only need to know how to recognize and write the Thai alphabet, you will also need to know how to say the letters correctly. The Multimedia Thai Language page has the entire Thai alphabet not only in charts but also in audio form so that you can hear each letter.
Build vocabulary. Start learning some actual Thai words and phrases. Write each word down, along with its meaning. Practice writing it several times, not only so that you can memorize it but also so that you will recognize it later. There are many vocabulary words and helpful phrases at the Into Asia Web page.
Learn grammar. Grammar is seldom anyone's favorite part of learning a language, but it's necessary. Luckily, Thai grammar is much less complicated than that of English and many other languages. You can find a good introduction to Thai grammar at the Into Asia Thai grammar page.
Read in Thai. Reading helps not only your ability to sound out and recognize vocabulary, but also your grammar. Reading is invaluable for teaching you how to form natural-sounding Thai sentences. There are a number of lessons on reading Thai as well as a huge Thai reading resources list at the Learning Thai website.
Listen to Thai. There are several podcasts available about learning Thai. If you have iTunes, you can subscribe to the Learn Thai podcast, Thai Lessons With Pink Chilli, or Thai Survival Phrases. If you don't have iTunes, all three also have their own Web sites where you can download some of the podcasts.