Before you start creating a character, think about some of the characters in fantasy literature that have inspired you the most. Make lists of some of your favorite character features and look to this when creating your character. When drawing inspiration from other people's works, though, take care to avoid creating a watered-down ripoff that smacks too strongly of someone else's creation. A good way to avoid this while keeping your inspiration is to create an amalgam of characters, combining features from two or more distinct figures to create someone totally new.
If your fantasy world contains non-human intelligent beings (e.g., elves, trolls or mermaids), decide which of these races your character belongs to. Think about how that will affect his personality and cultural upbringing. Ask yourself if he is a typical example of his race, if he's unusual, or if he's a combination of both in different areas.
Like any fictional character, a fantasy character should have some back story. This will make her more three-dimensional and give a fleshed-out explanation for why she's had the experiences she's had and gathered the knowledge she's gathered. This is also handy once you start to write, since opportunities will arise within the story for you to express her backstory in the form of her reactions to various aspects of the tale and the world.
In a fantasy setting, you will likely want to give your character abilities and talents he would not have in a non-fantasy setting. This is important to the creation of the character, but also the mechanics of your world. Magical abilities especially are something you want to take care with, since it's easy to make for a dull story if your characters have too much power with not enough limitations.
If your character has any pre-existing (i.e., dating to before the start of the story) relationships with other characters in the book, make some decisions about the nature of those relationships. This includes relationships with characters readers may not meet until some later point in the story. A three-dimensional character will behave differently with different people based on her relationships with them, and this will allow readers to see different sides of her personality.