My girlfriend's family raises sheep and goats. Her mom likes the idea of processing all the wool onsite instead of sending it out. But unwashed/raw wool is stinky--you have to scour the lanolin out of it & pick out any bits of straw/manure... Then it's a lot nicer to work with. Once it's been scoured, you send it through a picker (think big shredder thingy--see this
youtube video) to pull all the bits apart & fluff everything up. Then once that's done you lay it out in a layer or two, get a little bit of (the right kind of) soapy water on it, roll it in plastic (so it doesn't felt to itself where you don't want it to), tie it tightly, then roll & press it some way. You can approximate the donkey/roller press by tumbling it in the dryer with no heat for a while.
I went through some of these processes just to see what is was like. It seemed like a lot of work--I could have easily put in a full week or two's worth of work and gotten only close to a completed felt layer for my 6m yurt. So I went and spent a week's wages on woven wool-blend blanket material instead. But that was partially due to inefficiencies in that particular workshop area.
If you've been searching english language websites, you're bound to find mostly artistic/small felting setups--or ridiculously large industrial felt machines, which use an entirely different approach (needle felting). Here's a
video of the traditional mongolian process you mentioned, but you've probably seen it already. I don't know the details, but I've heard that you'd need to drag your felt roll something like 100 miles--maybe true, maybe not...
In terms of machines, something like
this roller setup is common for the non-industrial scale. Mind you, it's $1-5k, depending on the roller width. That particular website seems to have lots of felting tools and some books. There's
websites/rollers, too. The roller limits the width of felt that can be made though, unless you are particularly ingenious with resists.
I would suggest two places for finding more info--your local library may have some craft books on felting (near sewing & crocheting); you're local sewing/craft store might have classes (or books) on it. Neither of these would have exactly what you're looking for, but they could get you started. I would highly recommend making small felts (say 1-3 ft/1 m square or less) initially to learn the process. Then decide if the donkey is a good way to go