How does speed actually work in galaxy of heroes?

Speed is directly proportional to turn meter growth (there is a linear relationship), so there is no complicated formula like you might expect based on how other stats work. A character needs a turn meter of at least 1000 in order to take a turn.

After a character's turn their turn meter is decreased by 1000 (and any bonus is added as appropriate based on their skills and the ability used) and then the game advances one step — every character's turn meter is increased by the amount of their Speed stat (factoring in any buffs/debuffs). If any single character's turn meter hits or passes 1000, it's their turn. Otherwise, the game advances another step; repeat.

If two or more characters reach/pass 1000 turn meter at the same time, the one with the highest value goes first (since early February). If there is a tie, who goes first is random.