You will need to know the ranges of the three instruments and their open strings (vln GDAE; vla CGDA; vcl: CGDA an octave below the viola). You'll need to be able to read and write in alto clef (for the viola) and maybe tenor clef (for the cello if it plays high in its range).
You should have a basic idea of how string instruments are played: the difference between arco (bowed) and pizzicato (plucked); the difference between downbow and upbow; and for best results some idea of the range of different types of bowing techniques.
You should know how a string quartet rehearses: how a chamber music group rehearses and performs without a conductor.
Best advice: ask some string players to demonstrate how their instruments are played, and ask if you can be a fly on the wall at a string quartet rehearsal. Next best advice: listen to a lot of string quartets, with score in hand if possible.
Best of luck!