How do I reset a check engine light after repairing the problem?

Generally that's done with an OBD-II scanner, but there may be ways to clear the code without one. However, those methods are very specific to both the particular error that was generated and the implementation of the car's computer system. We would need to know both the code you fixed and the particular year, model, submodel if any, engine and transmission of your car. Some errors can be cleared by disconnecting the battery for 10 minutes, while others will clear themselves if the error is not encountered after a certain number of drive cycles.

I know that here in the US, most auto parts stores will scan your car for trouble codes for free, but I've never actually asked them if they would hit the little button on their scanner that clears the codes. May well be worth a try to see if you can sweet-talk them into clearing it for you.

Other than that, you can buy a very inexpensive bluetooth scanner online that works with a free app like Torque (Android and iOS) on your phone; some of them are only a couple of dollars like this one.

ELM327 Bluetooth 4.0 Car Engine Fault Code Reader Obd Scanner elm 327 V1.5 EOBD OBD II Dignostic Scanner For IOS/Android/PC - AliExpress