TL:DR; you won't, because it won't be worth the effort. As soon as asteroid mining becomes a practical way of providing resources for Earth, the value of metals will plummet.
Someone else will do the mining, and will probably sell you the raw metals on the cheap.
So, this is probably part economics, part safety and part orbital mechanics, and these things all kinda blur together.
Moving a refinery around the asteroid belt is energetically unfavourable, especially for a very large and heavy refinery. You have to inject yourself into a transfer orbit, trade off journey time for the amount of oomph you're prepared to impart to your refinery, wait a bit, and then rendezvous with the next prospect by matching orbits. Similarly, moving around large and heavy asteroids is going to be very challenging without the aid of large nuclear motors and lots of patience, and when you do start them moving they become a potentially serious hazard to all sorts of people and places, which limits where you might be allowed to move them to. Forget flying a billion tonnes of rock back to Mars or Earth... thats about as likely as you being allowed to drive a nuclear excavation charge through the centre of a major city.
Moving small rocks around is easier, but every single time you need to inject into a transfer orbit, coast, rendezvous, boost the rock into its own transfer orbit (probably with a suitable braking motor) and so on. Lots of hassle, lots of time, lots of rocks flying around at high speeds.
What you really want to do, then, is to claim the biggest unclaimed asteroid you can, and set up your refinery there, and suck it dry.
16 Psyche is one of the most massive bodies in the asteroid belt, weighing in at about 25 quadrillion tonnes. The surface of 16 Psyche seems to be about 90% metal, probably mostly nickel and iron, but no doubt there will be other heavy metals there. If the asteroid is as much as 1% iron by mass, it would have 250 trillion tonnes of iron. Current worldwide production of steel is under 2 billion tonnes a year, to give you some idea of the scale involved here (you'll need carbon to make the steel and 16 Psyche might not have enough, but there are plenty of carbonaceous asteroids out there you can mine for that). It could have more than a million years worth of iron and nickel, plus all sorts of "rare" metals (watch the value of gold and platinum crash). Other asteroids will provide vast quantities of aluminium and magnesium if 16 Psyche doesn't have enough of it.
What this probably means is that a few large asteroids like 16 Psyche will provide pretty much all the metal and mineral resources a growing civilisation could want, and even they represent a fraction of the belt's total reserves. The value of metal will just plummet, so there's simply no reason to worry about mining anything else. Just ask the people who are grinding up one of the big rocks to punt a nice of crude metal your way, probably with a fairly dumb robot tug attached. Probably cheap, and certainly a lot less hassle than faffing around with mining it all yourself.
There is an exception to be made for consumable resources. Ice will become quite a valuable thing, because it is useful for habitats and life support, cooling, shielding, as a source of deuterium for fusion and as reaction mass for all manner of rockets.
Ice of course needs much less fancy refining, assuming you can find a relatively pure source. You'll be wanting to fly it back to the places it will be used, probably by setting up a little deuterium refinery and nuclear rocket or mass driver to get it going. Flying around big masses in the inner system is something that is likely to be highly regulated for safety reasons, so it won't be the purview of little wildcat mining operations. If you try pointing something dinosaur-killer sized at Earth you're going to get a lot of Loudness, Lawyers and Lasers, and if you're lucky they'll be in that order.
Leave the ice-pushing to the grownups.