Never hang the painting in direct or strong sunlight.

Do not use Windex or other glass cleaners, they can fog the finish.

Do not wrap in bubblewrap, it can print on the surface!

The drip edges are quite fragile and can easily break off, so be  careful when handling the painting. 

If your painting came with a storage box, save the box for storing or transporting the painting.

Handle only by sides to minimize fingerprints.

Resin is a plastic, and can be cleaned like the "acrylic" in the following excellent excerpt from the Ridout Plastic website. 
"Never use a dry cloth or your hand to clean your acrylic! This rubs the dirt and dust INTO the acrylic as much as it rubs it OFF. First, blow the dust or dirt off, or use water and a soft cloth to float the dirt off. Then use a recommended cleaner to complete the job. Note: a mild solution of dish detergent and warm water takes off stubborn dirt easily without harming the acrylic if you've run out of Novus #1 or Brillianize."
More info can be found  here.

For my newer dot series with the matte finish, I've been using Aerospace 303 Protectorant as a finish.  It's formulated specifically for resin, and is widely available in the US and Canada in auto supply stores (ala Schucks).

Occasionally dust the surface, and reapply 303, whenever the surface loses its luster.

For more info:
303 Aerospace Protectant