What do we do?
This is a bit different for all D/s couples, from the degree to which they participate (mild to extreme) or the amount of time (just in the bedroom now and then to 24/7). My owner and I are in a 24/7 power exchange. What that entails is me asking him permission for anything I might do (deviating from what's expected), and doing anything he wants, as well as the concept of rewards, discipline (things to encourage me to be good), and punishment.
As more of a list of things we do, I'll start with the non-sexual. He is Sir or Master, I am whatever he wants to call me (generally, 'pet'). I do my chores and answer to him.
Sexually, there is roleplay fairly often, from rape play (consensual 'rape') to pet play (NOT anything to do with furries or bestiality) to incest play (pretending to be related) to age play (pretending there's a vast age difference). There is erotic pain from spanking, whipping, hitting, cropping, beating, pinching, or whatever else he wants (though of course, I must consent). He will piss on or in me for humiliation, and verbally humiliate me (simplified, things like "you like that, you fucking freak?"), or he'll spit on me, or so on. There's also forced, repeated orgasms until it becomes painful. All this turns me on like crazy, so it is definitely a part of sex, even if it can also stand alone.
The pain also transfers over into punishments for if I step out of place. Then (for example) a whipping is different; even if it is the same amount of pain, it is no longer pleasurable for either of us, just a way to put me back in my place. It's not pain, but it's generally some way of using me. Or punishment can just be making me be quiet and leave him be. Again, this is all consented to, and if I have a valid reason for misbehaving or safeword out, it won't happen.
What it feels like and what my life is like are pretty closely entwined. The most physical, literal sensations are up there already, pleasure and pain. It is amazing to submit, though, to know that I am giving myself over to be used however my owner wants, yet I am completely safe. As I understand for him, it is the same emotions, yet instead with the ability to do anything he wants to me, to use me, yet know he is making me feel whole at the same time. Power exchange and BDSM are about knowing each other, having communication,and pleasing each other. I am so happy when I submit. When I do rebel, if I am perhaps not feeling well and don't want to talk, being forced to kneel, apologize, and talk makes me remember how safe I am with him, and how close we are together. It is just somehow, intrinsically perfect.
Of course, for other people, it is just sexual kicks, or it is nothing. But this is what it is to us.
