Heating the old graphics up with a hair dryer makes them easier to remove.
Contact cleaner (or Windex or WD-40) is a good way to clean up the excess residue. Just make sure to wipe off any oily substance, like WD-40, before applying new graphics.
I use Windex on the back of new backgrounds/graphics during installation. That way you can slide the graphics around a little bit until you get them lined up right. Then begin from the center (or one side) and smooth the grahpics out with your fingers. Use a credit card to squeeze out the extra Windex. The graphics will also be easier to work with if you heat them up first (like sit them in the sun for a few hours). And a hair dryer will "seal" down small edges on the graphics, too.
Make sure to install graphics on warm plastics and in a warm place and let them cure for 24 hours if you can for the best results.