There are 12 side missions available in the game and in most cases you will be informed of the possibility to start a new one while you're playing through the main story (screen above). In a few cases however, you will have to first reach a certain point on the map or find an NPC to receive one. Detailed information on how to start a given quest can be of course found in the further part of the guide.
Keep in mind that you don't have to rush with side missions, as you will be able to return to them after finishing the main story. It of course doesn't mean that you should do that, as completing them will earn you experience needed to unlock new skills and gadgets.
You can check on the progress with given missions by turning on the Arkham City map and pressing X. In some cases, choosing a mission from the list will cause markers helpful in completing them to appear (e.g. the location of the next crime scene).