If you're like me, every present you wrap looks like it was put together as part of a state rehab program for people with severe nerve damage in their hands and arms. Our own Teresa Nielsen Hayden's excellent wrapping guide will set you straight.
Before you do anything else, take the price tags off the gifts. Do them all at once, right at the beginning. You won’t remember to check when you’re wrapping your fifth package and you’re up to your elbows in ribbons and gift cards.
Have a large flat clear area to work. If it’s the floor, sweep it and give it a quick swipe with a wet paper towel before getting down to work. Little bits of grit can do a surprising amount of damage to wrapping paper.
Have some bits of tape already torn off the roll and stuck down lightly by one corner on a hard, smooth object. You don’t want to be messing around with a roll of tape at crucial moments, because you need your hands for the paper.
(Note: most novice wrappers use too much tape. Wily old wrappers use all kinds of fastenings; for instance, hot glue guns and contact cement. For added geek value, you can either get great effects or get yourself into a whole lot of trouble with 3M Super 77 spray adhesive.)