I need to covert a 20 amp 250 v outlet to a 125 volt 20 amp outlet. The current breaker is a 20 amp double pole. There is a brown and orange wire fixed to the breaker and the outlet box has a brown, orange, green, and a capped grey wire. How would I go about completing this change correctly?

The colors are weird, so I'm not sure if your in the US. Not even sure the cable is rated for building wire.

So, FWIW if in the US. (read everything presented first)

The wires should have been taped the proper colors in the US which would have been black, red, white and green.

"coded" is defined as the ends being taped the proper color.

Green gets transferred to the ground screw of the new outlet. The box, if metal should also be connected to green in the previous and new case.

Code the grey wire white. Connect to neutral bus or gnd/neutral bus depending on the circumstances. This wire goes to the silver terminal of the 120 V outlet.

Pick one Brown or orange. Disconnect and cap one of them at both ends. Tape the other Black at both ends. Attach wire to brass screw at outlet end.

Now, you could in theory use one side of the 240 V breaker for a 120 outlet, but the correct way is to replace the breaker with a 120 V breaker and put a blank plate where the space was removed if necessary.

In the panel you will likely see one of two things:

1. All whites attached to one bar, all bares to another. This is generally for sub-panel wiring.

2. All whites and bares attached to the same bus. This is generally for main panel wiring.

In one case 2 white and green will attach to the same bus and in case 1 white will attach to whites and green will attach to bares.

Come back if the above information doesn't fit your situation.

Is this a residence? Are you sure this is 250 volts?

Brown, Orange, and Yellow with a gray neutral are typical 480/277 color code.

Definitely correct. B-O-Y-G colors are a red flag for DIY work.

If you have to ask about this that is a sure sign you should NOT be doing it considering the setting.

Call a qualified electrician who is experienced in working with 277/480v.