There are a few very good guides around the forums which describe how combos work.
I'll give you a quick run down.
When looking at the abilities of each ninja, there are around 4-5 skills. some of them will be labeled Chase. These are the skills which allow you to create combos.
Most combos start with the mystery skill, the skill that u activate with QWER. These skills will usually say something like "Cause Knockdown" etc. In this case "Knockdown" is the current condition for combo.
If you have something that causes knockdown, an ability which chases knockdown can combo with it.
Chases skills usually do two things, CHASE and then CAUSE which allow you to link up larger combos.
For example, your lightning main's ability is an AOE paralyze which causes Knockdown to a single target, Kurenai has a chase which chases knockdown and causes repulse. if you have Lai Giri on your main, you can chase the repulse and cause knockdown again. Thus you end with 3 combo as noone can chase knockdown again.