How to find out what radio frequency is being emitted?
If you have an old TV tuner around with you might get lucky matching the VHF/ UHF channel to the common narrow band transmitters or harmonics, but newer spread spectrum and rolling code encryption garage door openers are very secure.  It may result in some long nights scratching your head without some experience using TV tuners as spectrum analyzers with a scope.  It may lead to quit and start another profession.  Or it may inspire you to learn how to use a TV tuner as a scanner using a loop antenna for near field  signals.

First match the technology of the chips inside or brand or at least learn about garage door openers.

http://en.wikipedia.org/wiki/Garage_door_opener

I once proposed to Chrystler as a second source company, when they were buying from Delphi , who bought the technology for garage for openers for over a billion $ from this other company due to a hundred patents and muchos experience.  So this experience is not free nor easy.