Ummm... not sure where to begin with this one. Do you mean a DJ at an event like a wedding? In that case they usually just play different songs that are requested.
If you're talking about a DJ in a band or group (or solo), DJs do a lot of things:
1. Live Producer - when playing in a group, a DJ can simply select the tracks or samples that are part of a song that group is playing live.
2. Usually in a hip-hop live performance, a rapper/singer won't have a full band behind him, he'll just have a DJ in charge of providing the music - the beat/drums and all the instrumentals that go with it.