Take yourself seriously as a musician if you want to learn how to play jazz!
You have to believe in your own ability to play jazz, obviously you have to practice, but what you practice is going make you win!
Here it would be good if you have a knowledge of all the 12 major keys as scales (see previous posts) and by using the mode starting on the 6th note of the scale, will give you the relative minor key (as a natural minor scale). Note, sharpening the 7th note of that scale will give you the harmonic minor scale. For example, the scale of a minor A B C D E F G is the natural minor scale and A B C D E F G# is the harmonic minor scale - both are useful in jazz for improvisation. All the info below equally applies to the minor scales as well.
Once you know all twelve major scales, you can use those for practice on your instrument. Don't just play the scale straight from top to bottom or from bottom to top, start on different notes of the scale (you will then be playing the modes of the major scale, see post on scales).
Try playing every other note in C they will be C E G B D F A etc (you are now playing arpeggios!)
Go round the notes of each major scale until you are familiar with all twelve. Don't know the 12, try looking at http://www.piano-lessons-info.com/12-major-scales.html .
If you can't read music, don't worry, you'll find all twelve major scales sound the same ( Doh Ray Me Fah So La Te Doh) but each one starts on a different one of the twelve notes available to play your instrument.
C Db D Eb E F Gb G Ab A Bb B . In jazz, we generally (not always though) use flats instead of sharps (blame the reed instruments!)
Pick out the notes by ear on each of the starting notes. This actually gives you great 'ear training' for jazz playing!
All this work may be made easier by going on a jazz workshop and interacting with other players as they learn.