Purchase books or videos about music theory and study them. Start with basic classical music theory and gradually progress to music theory regarding jazz. Jazz requires a thorough knowledge of scales, keys modes and chords. The piano is a good instrument to learn jazz theory and harmony even if it's not your instrument.
Once you're familiar with how scales and key signatures work, practice all the major and minor scales on your instrument. Being able to play in any key will greatly facilitate your ability to improvise and accompany other musicians. A good tool for practicing and learning scales is the circle of fifths chart. (See the resource section for more information.)
Enroll in private lessons on your instrument. No matter what your skill level is, lessons with a more experienced musician will help. Check your local music store for information regarding music lessons. Either the music store will have instructors on site or the music store will have a roster of local music instructors. Also check with a university's performing arts center for lesson advertisements, or ask a faculty jazz instructor.
Purchase a fake book. A fake book is a collection of songs and contains the basic melody, accompanying chords and lyrics (Reference 2). After you've purchased a fake book, start learning a few songs by playing the basic chords. This will prepare you for playing in a combo. Many types of fake books have been published, but the best-selling jazz book is called the "Real Book" and is published by Hal Leonard Publishing (Reference 1).
Find or organize a jazz combo with members close to your skill level. Jazz thrives in a collaborative environment. Performing with others will greatly increase your musical skills and boost your confidence as a musician. A jazz combo could be anywhere from two people to a big band. If you live near a community college, see if they offer jazz combo courses. Many community members who are not degree students enroll in jazz combos offered by community colleges. Another way to find collaborators is to post an add on Craigslist or a music classified site such as Bandmix.