My Scizor is currently running Technician but I don't know how it works. I've read about it on Serebii and it says that any moves with a base power of 60 or lower are given a 50% boost. My Scizor has the moves Bullet Punch, Aerial Ace, Fury Cutter and U-Turn and is holding a Choice Band. Bullet Punch has 40 power and STAB makes it 60. Does Technician still boost it? And would the boost be an added 20 power or 30? And if the power is added by 20-30, making Bullet Punch's power 80-90, would the Choice Band raise it to 120-135? And U-Turn's base power is 70 and since it's higher than 60, Technician doesn't work on it, but would STAB make it 105? And would Choice Band raise it to 140-152.5?
When determining whether or not Technician will boost a move, it only looks at the original base power of the move. So Technician will always boost Bullet Punch.
It stacks multiplicatively with things like STAB and being super-effective. Scizor with Technician using Bullet Punch will use it as if it has 90 base power. 40 + 50% for Technician is 60, and then adding 50% on top of that for STAB brings it to 90.
The choice band doesn't increase the base power of the move, but rather effectively increases the pokemon attack stat. That also stacks multiplicatively with the base power, however, so it does effectively increase the entire new base power of 90 by 50%.
U-Turn is not affected by Technician, but is increased by STAB to 105, and then choice band's attack bonus effectively stacks with it again.