jazz uses mostly chords constructed on the 1 - 3 - 5 - 7, these are basic 4 note chords, these chords can have extensions or tensions which are added to the base chord, there are different extensions to the different chords for example a dom7 chord may have the 13,9,b13,b9,b5,#9,b9.
also some of the tensions will fit better on chord progressions. in other cases the composer will hint you to use extension by placing the word "alt" (altered) over a dom7 chord