Airbag light stays on, how do I fix this myself with no cost or little cost?

If you haven't had the error code read from the cars SRS Airbag Computer Control Module, take the car to your friendly auto parts retailer and have the code read. Most parts suppliers will provide a complementary scan.

If the light comes on a second or two after the key is turned on it is an indication that the SRS computer has failed a system check.
The attached image shows components checked during the SRS diagnostics startup check. They check the wiring for bad connections and the airbag explosive charge to confirm the connections and charge is ready..

Having the error code data will give you an indication of the cost associated with the repair. With the light lit the saftey restraint is deactivated and the problem should be corrected. Many cars have tensioners that tighten the seat belt during a crash. Connections to these components along with the seat presence switches can have connection problems under and around the seats.

SRS remains charged even when the power to the SRS computer is removed. This makes sense when you think about a crash where the electrical systems fails at the instant the system needs to deploy the airbag!!

These systems need to be serviced only by a qualified technician. The Airbags can deploy without warning as when you are working on the system and not follow the required procedures.
Hope this helps?