If you have a non-contact voltage detector, plug in the string, follow the hot wire till you lose voltage, replace that bulb.
If you don't have a non-contact voltage detector, throw the string away, wait for the after-Christmas clearance sale and buy a new string for under $2. Buy several.
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"Well, I've wrestled with reality for 35 years, Doctor, and I'm happy to state I finally won out over it." Elwood P. Dowd
What do you mean with repair it? Christmas light are supposed to work for one christmas! If it's new, take it back for another one. If its the second year, you are in the average failure rate. If its the third one, you already won some money. After three years... Oh yeah, congratulations, contact the manufacturer because he will be amazed!
I don't have a non-contact voltage detector, but that a great idea, I may consider investing in one. Here is the process I use. Get the replacement bulb. Pull the first light that is not lit and replace with the good replacement bulb. Pull the next bulb and replace with the first bulb. Work your way down the string of lights. By process of elimination, you will find and replace the bad bulb.
This seems like a lot of work, but it goes quick and is effective...unless you have two bad bulbs...