What's the trick to wrapping tightly in plastic wrap?
The wrap used in most grocery stores isn't the same as your household wrap.

Most of the consumer brands of plastic "cling" wrap are now formulated from low-density polyethylene. It's rolled very thin to give you the best price per unit of length, and has reasonable stickyness.

Most stores use a product called "meat film" which is most commonly made from PVC. It's a little thicker, more wrinkle-resistant to give the product contained inside a better appearance, and it's stickier. 

The other thing that grocery stores do to make the seal better is they use a heat sealer on the plastic. These are heated pads where they'll place a wrapped piece of plastic for a few seconds. It's not enough heat to melt the plastic, so in most cases you can still pull it apart, but it is just enough to shrink the joint together, and pull it taut across the front of the packaging.