Step 1 -- unless you have a tow package and heavy-duty flasher, the flasher is load sensitive. If a turn indicator bulb is burned out, the flasher won't flash, it will stay lit constantly. Check your bulbs.
Step 2 -- if all the bulbs are good, replace the flasher. There are two, one for the hazard warning lights and one for the turn indicators. Don't recall which is which. Both are in the fuse panel under the dash above the driver's left foot. Turn on the 4-ways and touch each one to see which is clicking. The other will be the turn signal flasher. They interchange, so for a quick test you can just swap 'em. But the hazard flasher is the heavy duty type and is not load sensitive. Don't leave a load sensitive flasher in the hazard socket.