I may have posted this already but due to many a request:
Uncle Sixty's Easy V Brake Set Up
Release the brake cable at the brake arms.
At the brake lever, turn the barrel adjuster all the way in and then turn it out 6-7 complete revolutions... I find there is a little variance between brake models.
Make sure that all the cable ferules are seated properly and that none have slipped out.
Going back to the brake arms, snug up the brake cable so that both brake pads are hitting the rim and then tighten the cable, the wheel should not move.
Go back to the lever and screw the barrel adjuster back in and your brake spacing should be nearly perfect.
The wheel should spin freely, if not, the brakes may need to be centered.
Make any needed centering adjustments at the brake by using the small adjustment screws on the caliper arm, these control the return spring tension. You usually adjust these in tandem in that if you loosen one, you also tighten the other a little and with new brakes both screws may need to be tightened to increase the spring tension. If the springs are in similar condition the screws should be close to each other in where they are set.
If this adjustment is problematic you may need to take the exposed spring on the weak side, unclip it and bend out out a little to increase it's tension.
After all this is done the brake lever should max out at no more than 50% of it's travel, braking should be quick and firm, and there should be no issue releasing the brake by detaching the noodle.
Give the lever 10 hard pulls to ensure that there is no slippage and that no ferules have unseated themselves.