Any chord that is a closed form ( that means no open strings; all fretted notes ) may be moved up and down the neck. What you need to do is learn two things. First, what note ( or notes ) in the chord form is the root note, and second, how to correlate that knowledge with where on the fretboard you are.
For example, take a garden variety 1st position F Major chord. You have two F's in the chord; on the 4th and 1st string. Either of these are considered the root note. Slide the entire chord up to the 5th fret, you now have an A Major chord.
In jazz, lots of times they are playing only partial chords, or rootless chords, and almost always some type of extended chord ( a chord containing more than just the 1-3-5 notes, usually has a 7th and some sort of "color" note, like a 9th, 13th, #11, etc. ). This is a bit trickier, because you need to know the chord well enough to know where the root would be, even though you probably aren't playing it.
A good jazz chord /theory book would be immensely helpful to you, if you relly want to delve into this. It's a huge subject. I would suggest you visit www.jodyfisher.com
, and check out his book on Chord Melody ( that is what this type of playing is called ). It's the best one I have ever found.