Let's say that the game involves you taking on the role of an FBI agent.
A major part of identifying with a role involves learning the skill set of that role. If you can do a heart transplant, there's a good chance you'll feel like a heart surgeon. Of course, this education works particularly well if it takes place during early missions or training programs that offer genuine suspense and lots of fun.
What are the skill sets of the agent? Surveillance? Hand-to-hand combat? Mastery of a variety of weapons?
As we master the skills and tools of a trade, we begin to assume the identity that goes with them.
There are a number of other ways to encourage a player to become emotionally caught up in a role. The following sections describe a few. I'm certainly not saying you should use every one of these. But, while some of these can be used in combination, you'll note that many of them can't.