You might find yourself needing to research a facet of your character's situation. In a manuscript of mine, my main character lost her husband the day before their one year anniversary. I haven't personally dealt with a loss of this magnitude, so if it's possible, I'll talk to people who have. And I'll talk to a friend of mine who's a life coach to gather ideas about how she might direct my main character. Plus there are lots of books about getting over a loss like that. I could check those out. While everything might not apply, or while some of the advice might be bad, it's still advice your character might receive.
Another good way to research how your character might feel about something is to look at your life through their eyes. This exercise came to me one day while I was working on So Over It. I was at the grocery store with my daughter, who was about 8 months old at the time. She was wearing a Kansas City Royals shirt and the cashier said, "Your daddy must be a fan." This is true and therefore didn't bother me ... but that would be a painful comment for one of my characters, a teen mother who has nothing to do with her baby's father, to hear.
Or, for the manuscript about the woman who unexpectedly loses her husband, I'll sometimes look around our house and think, "What if I lost my husband right now? What kind of things would be left undone? What of his belongings would be sitting out, anticipating his return?" (These kinds of morbid thoughts sometimes keep me up at night and frustrate my husband, but they strengthen the emotions I put on the page.)
Sometimes you're just looking to build your knowledge base. The character in my WIP has grown up in a foodie household. Her dad has started several successful restaurants, and her mom is a food critic/columnist. And while my character doesn't talk about braising, julienning, and the benefits of pasture-raised beef in any of the scenes, these are things she's grown up hearing about. So right now, I'm reading food books. A lot of food books. And a lot of food blogs. And we'll be trying lots of new dishes in my house.
Next we'll talk about researching all that "other stuff."
If you have other ideas for researching your character's inner-workings, please share!