Mostly, I come up with a name or idea and try to find powers that fit it.
Sometimes I play around in the character editor until I find a look that I like, and try to find a background and power that fits with it.
Case study: Bleeding Sun.
While reading DC's "Trinity" maxiseries (the most recent one), I was inspired by the character "Sun Chained In Ink", who used magic to imprison a sun in the tattoos on his body.
I decided to make a magical character with sun-based powers. After a while I came up with a name that stuck in my mind: Bleeding Sun. It sounded colourful and dangerous, without being evil, like someone who "bled" (siphoned) the Sun's powers for her own use.
I could have made the primary power heat-based, but that would have been too obvious. No, the Sun has another power that is just as great: it's enormous gravitational field, which keeps the entire solar system in place. So the primary power was going to be gravity-based, and the secondary heat-based. The only thing that fit was a Gravity/Thermal Controller.
Then I started thinking... if you can base a character on the properties of the Sun, why not on the planets of the Solar System? Thus, the Ecliptic Order was born, an ancient school of magic whose adepts specialise in drawing power from different heavenly bodies.
Now, you have all heard of an animated series that names it's characters after different bodies in the solar system: Sailor Moon. Of course, I couldn't resist putting an evil twist to that theme, and tried to create a male character in a sailor's outfit named Sailor Uranus.
Unfortunately, Sailor Uranus was not available, so I had to settle for First Mate. But at least I could put a small Uranus symbol on his chest.