From where you beam into Earth starbase, head to your LEFT. Keep going past the bar, and into the next big room. Against the far wall is the guy where you can change your uniform and character looks...but it costs credits.
Yep, what they've said. Head to Earth Spacedock and go to Requisitions. The Cardassian-looking guy there will let you alter your uniform. But it costs credits so if you're just starting out you probably won't be able to do much more than small changes.