How far can a character move in combat?

Quickness affects your chance to hit with Ranged Attacks and to Dodge. I haven't played a Troll, but I think base move speed for every characters is the same. There are a few ways you can increase move speed for your character:

• Equip clothes that give + to move speed (Stealth Suit, Ninja Outfit,etc give +1; Street Brawler gives +2)
• There is at least one Cyber Implant that gives + to move speed (Wired Reflex)
• Racoon Totem spell gives +2 to movement for all allies within range.
• If your character focuses on Chi Casting, the Stride spell gives +4 to move

The base movement is 6 squares per Action Point. This is true for all races and stats (e.g. Quickness 9 doesn't change it). The only things that affect it are things like what Jeremy shared that specifically mention bonus to Movement (Blur spell, Hydraulic Jacks, some drugs, etc.).