Hello and welcome to JustAnswer!
If the problem that caused the engine light to turn on is fixed, then the engine light will go off by itself after the problem area has passed a test three times in a row. Since you replaced the gas cap I'm assuming you had an evaporative emissions leak, in that cause it would take about three days of regular driving for the engine light to go off on it's own.
For immediate results you could disconnect the battery. This would clear the engine controller's memory and the light would be off when you restarted it.
The codes can also be cleared by a code reader or scan tool, Autozone would be able to clear it for you just as they read the code for you.
Autozone's code reader will clear codes just the same as it will read them. all they have to do is push one extra button.
The only other ways are the ones that I have mentioned. A scan tool, code reader, disconnecting the battery, or allowing the light to go out naturally are the only ways to turn it off.
Cycling the key from off to on three times will display fault codes in the odometer display, and pressing and holding the trip odometer reset button will initiate an instrument cluster self test and display instrument cluster related codes, but neither of these things will clear codes and turn the light off.