Dodging in Unreal and Unreal Tournament is a sort of Equivalent to Bunnyjumping in QW and Strafejumping in Q2/Q3/CS. Experienced players can go around the map much faster using this technique, because the dodgespeed is 600 unreal units per second, which is 1.5 times the normal movement speed.
Something you should know is, that the velocity component vertical to your dodge move isn`t changed, so the fastest method is to walk forward/backward, but dodge sideways, or the opposite of that. This means, that you walk forward for example, then do an approximately 56 degree turn to the left (arctan(1.5)) and dodge right as fast as possible, so that you build up as few velocity to the right as possible before dodging.
"dodging done right"
After dodging you turn back until you can dodge again. Like this you can build up a theoretical maximum of 721 unreal units per second opposed to the 600 uu/s when dodging normally and 400 uu/s, when running.
I have recorded a demo to show what I am talking about.
You should also learn to make use of height differences. While in the air there is no friction, so you keep the high speed gained from dodging. That`s why someone who runs up a hill and dodges down is faster, than a player running straight forward.
Unlike Bunnyjumping/Strafejumping dodging can also be very useful in fights. You can either quickly evade projectiles, like rockets, flak shells or plasma/pulse balls. Or you can irritate your opponent, so that he is losing his lock when shooting with instant hit weapons. It can also turn out to your disadvantage though, once you started dodging there is no way you can stop in mid-air, so you are easy to predict.
Besides that you can do jumps, that are impossible with the normal jump button, because when dodging you jump far, not high.