The wrong way to twist is holding the ends tights with a vice/drill/whatever and turning it. "Twist" really is the wrong motion to use entirely, because what that does is physically twist the wire and it wants to untwist itself back to original state (think like you're winding up a big spring).
You should be simply passing the wires across each other repeatedly. Fix the wires at one end in a vice, then hold the wires one in each hand, pass over to the opposite hands pulling lightly after ever couple passes. This is much slower, but is really the only way to do it. What this does is get the wires to wrap around each other*, but not actually "twist" so now they won't try to unravel themselves. You can control the amount of twist by the angle and how tightly you pull the ends.
*for those wondering, it's more of a bending that happens to move in a circular path, and the amount of energy stored in the bending is minimal and transverse to the longitudinal axis so it is all spread out, whereas the twisting stresses are all quite large and additive along the axis.
Edited by Armaegis - Today at 10:43 pm