Help Please? Switching to an Unlocked Phone

Hi. I am currently with Bell, but my phone is messing up big time. I have an unlocked phone that I want to switch to but I am not sure how. I know that with Rogers phones all you need to do is put your SIM card into the new phone and it should work. However I am unclear about whether Bell phones work the same way. If someone has an answer that would be really great!

Thanks