Just like in any case of an action game, with an open world, in the inFamous: Second Son you can deal with main (story) quests, as well as sidequests, although the latter are much less important that it might seem. The main quests are form single, solid series, but as soon as you finish the first stage, after reaching the city (Welcome to Seattle), you won't have to rush with other main quests. In the meantime, you can take on some minor errands, or additional activities, which are thoroughly described in the "Step 8" section. If you want to start another main quest, you will have to find the marker on the map, get to it and confirm it.
Two things related to main quests are worth mentioning:
1) Read the information displayed after completing every main task very carefully. The next main mission isn't always available from the start - sometimes the game forces you to take on some of the additional activities, or to roam around the city a little more.
2) Some of the main missions can be "altered", according to your karma - it will be different for a hero (good karma) and a villain (bad karma). More on this correlations can be found in the "Step 5" section. The walkthrough takes into account both playstyles.
As it was mentioned before, the sidequests are marginal for the story, as they are a number of random events, which Delsin can be a witness of during free roaming (an example can be seen on the above screenshot). This events are connected with the acquisition of good (blue icons) and bad (red icons) karma. They appear randomly and you don't have to take them on the moment you stumble upon them, as they won't disappear with time if you ignore them. What is more, a great number of them can be accomplished more than once, accumulating a bigger pool of good / bad karma in the process.