From 
First, slide back the plastic covering on the plug to check the fuse. Some strings have more than one fuse, in which case they’ll be next to each other. Replace any blown fuses. New ones are available where holiday lights are sold and at some electronics stores.
Second, test the bulbs with an inexpensive tester (less than $10), available where holiday lights are sold and online. Usually, changing a problem bulb (or tightening it) will fix the entire strand. The tester will indicate which bulbs are bad and need to be replaced. (For the tester to work, the lights must be plugged into the electrical outlet correctly—the narrow “hot” blade into the narrow slot and the wide neutral blade into the wide slot.)
Some testers work by having you slide each bulb through a hole. With other testers, you simply touch each bulb. You can test an entire strand in a few minutes. Sometimes you have two or more defective bulbs, so only identifying one bad bulb may not fix the problem.