For fantasy settings: I bang syllables together until I come up with something that sounds good. :P
OK, I start out with a vague idea of sound, like "this language has many sibilants and more aei than ou", or if I have names in that setting already I try to make up more names so they sound like they all fit together, but, basically, yeah.
For the real-world based setting, I try to pick names - well, first names, at least - that work both in German and English (because the characters are German, but I write stuff in English.)
Sort-of-relevant chatbit of a brainstorming session in chat:
* Anke calls her Wstfgl
* Anke would actually use Foigu, if that didn't look like a bad pun on fuego
Anke: (no, not really)
Anke: And she can have a brother called Rhythm! :D
Snog: Geeky! I approve.
Anke: or, no, a sister named Rhythm. Who marries someone named Algo!
Anke: (I'll so go to hell for this.)
Snog: (I'll come with you, laughing.)
Snog: And one of them has to be called Poly.
Anke: someone's kid
Anke: Twin of Gamy
* Snog dies XD
Anke: ... and Loga and Mael must have a son named Strom
("Loga" indeed stuck. Mael had been named beforehand already. The rest didn't happen.)