I think I'd replace the turn signal flasher. It's just a little bi-metal switch and can go bad easily.
check your fuses first, then check your bulbs and then your relay.
Check the bulbs, check the fuse then check the switch.
Bad switch? Bad relay/ Breaker tripped?
Check the bulbs they are double filamented with the smaller for stop and turn signals
Check fuse,bulbs, flasher
Check the fuses and the bulbs.
Faulty light bulbs, damaged engine.
Either the flasher or the turn signal switch is bad.
Epic Failure.
I can't be 100 % sure as I'm not real familiar with your model, but my earlier Sunfire's bulbs are accessed from inside the trunk, You'll have to pull the carpet away from the body, then twist out the bulb holders.
Check fuse, bulbs, and flasher relay.
I guess I am what you would call mechanically challenged, however this has happened to me many times and it has always been a blown fuse or bulb. Your car manual should give you the location and type of fuse or bulbs you will need. This is just a personal opinion.Viper1