What I should do about taking my birth control while in a different time zone?

Time zone. Just keep an alarm on your cell phone to ring every 24 hrs and will let you know when is time to take your pill. You need basically to take a pill every 24 hours.
Daily is usually ok. For a combined oral pill with both estrogen and progesterone, taking it at the similar time, reguarless of what time zone is ok. But if you are on a Progesterone only pill, you need to be more precise at try to take it near the same time you would when you are in your home time zone.