Look for the Tag
Check the tag for washing directions. There usually is a manufacturer's label with washing directions on the inner wrist of cycling gloves.
Cold Water, Please
If there isn't a tag or you've lost the instructions, washing in cold water with mild detergent should be fine. Be careful to separate light and dark colors, and use the delicate cycle on your washing machine.
Before placing bicycle gloves in the washer, be sure to securely close any Velcro straps. Make sure that none of the rough hooking Velcro is uncovered, or it will latch onto other clothing in the wash.
Hang your cycling gloves to dry. They will last longer if you do not dry them in the dryer. Some cycling gloves also have leather pads, and they might crack or shrink in the dryer.
Gentle hand washing is also an option. It takes a little more of your time than machine washing, but it might prolong your gloves' life. Use delicate fabric wash and cool water in a sink. Rinse well, and hang your gloves to dry.