A recipe is asking for "canned black beans, drained, rinsed and warmed".
I've never just heated up beans by themselves. How do I warm up these beans without using a microwave? Do I heat them up in a pan with some butter/oil or in simmering water?
I'd use a microwave but you've ruled that out. Taking "warmed" literally as meaning made warm but not hot, you could put them in a bowl, cover with boiling water and wait a few minutes. I suspect that you actually want them hot, in which case you could put them in a small pan, pour over boiling water, cover, and return to the boil for a few minutes. If you don't have an electric kettle, just boil a small pan of water and tip the beans in.
Pour the can into a small pot (without draining or rinsing), and heat on the stove over medium-low heat with a lid on, stirring/shaking frequently.
This is pretty common, even for just heating beans to be eaten. Such as black beans on the side of some tacos or something.
There are a couple of different approaches I might take:
Done two days ago. Open, drain, plunge beans in hot water, drain again.