This one is pretty simple and should come naturally through campaign, but if you are like me and jumped straight into multiplayer and only played one hero, you might skip it.
All heroes level up and get skill points through completing objectives and killing enemies. Easiest way I found was to replay the HARM room missions with different heroes at the top of the Helicarrier map in Avenger's Initiative if you want it quickly. There are tons of enemies and it is scaled to your power level. However, no gear drops so you will not level up your power level here.