Definitely most of the Delsin's powers and abilities (offensive as well as defensive ones), is connected with the usage of the Smoke power. The Smoke allows you to move around the area easier and faster ("teleportation", red ventilation shaft usage, floating above the ground), which was thoroughly described in the "Step 1" section. In the case of the offensive actions, the fire element takes some attention, because some of the projectiles you shoot deal fire damage or explode on contact.
As far as exploration-like abilities doesn't consume Delsin's smoke supply, launching offensive abilities requires you to have a certain amount of smoke collected beforehand, which acts as a resource in the game. The current supply of smoke is displayed on a bar, in the bottom left corner of the screen and after depleting it, Delsin will be left with only the basic attacks (his chain, for instance), with which he won't be able to do much. It is crucial to observe the reserves of smoke and react accordingly.
The game world has a number of smoke sources, but as the action of the game takes place in a city, you will be acquiring it mostly from car wreckages. You don't have to look around for wreckages, as you can simply destroy the nearby "fine" cars - they will emit smoke after doing so.
Car wreckages aren't the only source of smoke. Another good idea is getting on building rooftops (by using the red ventilation shaft, if possible). On most of the rooftops, you will encounter chimneys, from where a smoke will be emitted (the above screenshot show such a chimney). An advantage to that, is that most enemies won't be able to continue chasing you on rooftops - besides replenishing your smoke supply, you can regenerate your health and get back into the fight refreshed.