Simple tester checks Christmas-tree lights article gives you ideas how to test mains powered Christmas lights. The article presents a simple test circuit. Some more testing ideas can be found at Christmas Lights and How to Fix Them web page.
LED lights are becoming more and more popular for common in Christmas lights for many good reasons. They consume considerably less energy than traditional light bulbs and fail much less often. If you LED lights fail, you can find ideas how to fix then at LED Christmas Lights and How to Fix Them web page.