When I use my mobile phone abroad, can I choose one mobile operator over another?

If your GSM mobile service plans supports international roaming, your mobile phone will only work in networks that have a roaming agreement with your home carrier. A list of preferred international carriers is stored in the SIM, and your phone automatically connects to networks based on the preferred order established by your carrier. Some carriers allow you to manually edit this preferred list. Try going to the phone settings menu on your mobile (please refer to your manual) and under the menu usually called Network Selection you’ll be prompted to make a network selection from the offered list.

Another option is to switch the SIM and use a prepaid local phone network while in that country. This requires that your phone is unlocked. For more information see, So what’s the advantage of an open or unlocked phone? and Can I move my cell phone service just by moving my SIM to a new phone?