Take out all of the bulbs and the fuse. Put a ohm meter on the fuse side that the lights are hooked to. It should read an open. If it reads a short then you have either a bare wire touching metal or a shorted light socket.
If you get a reading on the meter with the bulbs out then you may have a corroded light socket.
If it reads open, put the bulbs back in one at a time until it blows the fuse. That is the place to start looking for the problem.
Make sure the fuse you are using is the correct size fuse.
The above is very good information.
Does the fuse blow right away.
Does the fuse blow as soon as the flasher is put on.
Does the fuse blow shortly after the flasher starts.
A shorted lamp will blow the fuse right away.
Craig Clayton
Craig and Gary are right on with their advice. Depending on how you turn the signals on such as in a steering column where the wires enter is a likely place. As is a defective switch that might be cracked.