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:
Drain, rinse, place in pan on hilltop or microwave. Add small amount of low sodium chicken broth. Works great with canned, drained green beans.
Done two days ago. Open, drain, plunge beans in hot water, drain again.