To walk a good jazz line is the one of the hardest things for a bassist to do, but it is also the most exemplary role of a good bassist. Together with the drummer, the bassist controls the cadence, movement, tempo, and overall feel of a piece. The bassist either consciously or unconsciously steers the piece from beginning to end. When done successfully, the bassist can keep the listener at the edge of their seat the entire song. A hundred soloists can take turns and a good bassist still keeps things fresh.

However, you have to start somewhere. I've learned how to walk both with help from my teacher and from figuring things out for myself, and want to show you the progression I followed. Some lessons will you show you a couple sample lines, but few tell you what do when you have 30 seconds to learn a piece before laying it a dozen times through. I'm going to try and do that.

I'll try to cover every aspect of walking, but there are a couple things you have to know already.
The first are the notes of the fretboard. In some kinds of music you can get away with only knowing one position for each note, if that, but you should know the whole thing if you really want to play jazz.
Second, you should learn your scales. If I refer to the "fifth", or the "seventh", you should know that I mean the fifth or seventh degree of a particular scale. (A good start would be the major scale, minor scale, major and minor pentatonics, blues, mixolydian, and locrian. Ideally, you would learn all your modes, which are under the "bassics" section here at AB.)
Also, the ability to read sheet music is not absolutely necessary but will help you immensely.