As was said, look in the spell descriptions to see what combos off of what. For mages it should be easy to figure out since all the combos are going from a lower to higher tier spell of the same element.

Since you are at least 18 THM, you should have Thundara by now. When you use Thunder (and are not resisted- this is important) you should get that "Readying Combo" icon on the top of your screen and Thundara on your Action Bar will get a purple glow around it. Hitting Thundara at this point will give you its combo effect: Increased damage and Reduced recast time if Thundara's Stun effect fails to land. (Also just FYI, it's best to use Parsimony right before landing the final hit on your Combo).

For other Combos, keep in mind that you have to fulfill all bonus conditions for the move in order to start the combo, and you can't start combos from the middle.

Example: Concussive Blow does more damage from the front, so you have to use it while in front of the enemy to start a Combo.

Example 2: The thunder spell line combo goes Thunder > Thundara > Thundaga. You can't make a combo starting from Thundara to Thundaga, you have to start with Thunder.

It helps to rearrange your action bar so these moves are close together if you play with a gamepad. It probably helps if you're on keyboard, too.