It's quite simple really.
You obviously chain moves by using the same attack button.
If you connect a blow and have only pressed the button once (instead of repeatedly pressing) it scores a critical hit, which ups the score.
You raise the combo multiplyer by linking other moves into the combination which are.
1.Punch
2.Counter
3.Take Down
4.Throw
5.Somersault Evade
6.Ground Take Down
7.Batarang
8.Stun
9.Batclaw
If you get all 9 in one combo you get a large bonus. Batarangs and the Batclaw can be activated by tapping the respective shoulder button once (on PS3).
Normally a good way to start is Batclaw ->Stun with Cape ->Somesault evade over the stunned thug->then begin the attack and link the other moves in from there.
Ideally knock the last thug down with the Batarang and then use the ground takedown to finish the combo.
Hope that helps