Unfortunately the built-in diagnostic function on the vehicle is only capable of reading out codes, and not clearing them.

In order to clear the codes to turn off the service engine soon light, you will need to use a scantool or code reader with a 'clear codes' function.
If you live in any state outside of California, most big-chain auto parts stores (AutoZone, OReilly, etc) offer free code scanning and clearing. Just take the vehicle in to have the codes read, and ask them to clear them as your repairs have already been made.

Alternatively, unhooking the negative battery cable for 3 minutes will reset any codes set or pending. If your problem is not repaired however, the light will return. You will also lose any radio presets, etc, this way.

During normal driving, most codes will allow the light to go out within 3-5 full temperature drive cycles if the problem has been repaired.