Good fabric deserves a little care. Here's the quick version, sorted by what you're wearing.
Heavyweight cotton (oversized tees, acid wash)
Machine wash cold, skip the bleach, tumble dry low or line dry. Acid-washed pieces should be washed separately for the first couple of washes so the color settles.
Supima cotton
Gentle cold cycle, line dry if you can. Supima's long fibers are what make it soft, and gentle washing keeps it that way longer.
Terry knit (Bloom line)
Turn it inside out before washing. Reshape and dry flat rather than tumble drying on high heat, that's what protects the looped texture.
Embroidered pieces
Wash inside out on a gentle cold cycle to protect the stitching, skip the tumble dryer, and iron on the reverse side only, never directly over the embroidery.
The short version across almost everything: cold water, no bleach, low heat. Your Coolothe pieces will outlast the trend cycle if you let them.