If the flashers work on one side the flasher unit is good. Check the bulbs and connections at the bulbs on the side that doesn't work. After that there is a possibility that the problem is in the turn signal switch itself. You will need a wiring diagram specific to your make and year of car and a good volt/ohm meter to start tracing the electrical circuit. Autozone have some popular workshop manuals for free on line once you register (for free) on their website http://bit.ly/autozone_repair_info .There is a company that independent auto repair shops "buy" their information from that offer a very reasonable service to do it yourselvers. You get a one year subscription to year make and model specific repair procedures, service bulletins, component locations, wiring diagrams ect.... great quality information same as the professionals have ,much better than generic workshop manuals from parts stores, much cheaper than the factory manual. http://bit.ly/alldata_repair_manuals or try http://bit.ly/mitchell_repair_manuals_online and get an online repair manual subscription.
actually your wrong the panel just above your feet comes of with three 10mm screws. you have to get on your back lay on the floor board of the driver side. underneath next to all the wiring there are two flashers one on the left side and one on the right side of the steering column. that will fix your problem