I bought a 2 hold Refinery and a laser and headed out to Styx Site 6. In my Sidewinder if I wanted to keep my basic discovery scanner (which I thought I might have needed for the mining), I had to dump my shields. You don't need the basic discovery scanner, by the way, for mining.
Pretty dramatic, all the rocky asteroids rotating slowly in the brightness of a very close by sun.
My observations:
You can't target individual asteroids. Asteroids thus have no names and no way to identify one from the other. There is no way to scan an asteroid for minerals before mining.
Asteroid "fields" are no where near as crowded as the rings of a planet. They're probably 1000m+ away from each other, and all of them I've seen so far are about 1/3rd as big as a station. If you get jumped in an asteroid "field", you should play it pretty much like you're in deep space. Not like you can do some fancy and daring Empire Strikes Back flying to avoid enemies, but I suppose you could circle strafe around an asteroid to confuse the enemy.
Each asteroid only spits out about 10 chunks, sometimes less. Then you have to move onto a new asteroid, which, since you can't target the old asteroid, becomes a bit confusing. There is no notification that the asteroid is "empty" - you'll just stop seeing chunks pop out, and then you move on. You could easily head towards an asteroid you've already mined and have no idea after several asteroids worth of mining, because they all look the same and there's no way to tell them apart. I would assume the asteroids replenish their minerals every xx minutes to keep them "stocked".
You don't have to keep the laser in one spot. I thought this to be odd. The asteroid is spinning, so you can just point in one spot and let your mining laser paint a pretty series of lines all over it, and watch for the chunks to spit out. Originally I thought you had to keep the laser focused on one spot which was challenging as the rock is rotating.
After you have the chunks, open your scoop and go collect them. Don't hit the asteroid!
Chunks fly out and presumably tell you how much % of 1T worth of a material they contain, but I don't find that number to be accurate. I'm not sure what that % means. They could also contain other minerals.
You won't be hurting for cargo hold space, you'll be hurting for Refinery space. It takes 10+ chunks to make 1 ton of minerals. Problem is, you have only 2 refinery spots. If you mine one asteroid and it spits out Gallium, you now have say 10% of 1T of Gallium sitting in your refinery. In order to "clear" that 10% of Gallium and reclaim your refinery spot, you either need 90% more chunks to make 1T, or you need to vent it. Say you bail on your Gallium asteroid and go next door - and this asteroid is now spitting out Silver. Now you have 10% of 1T of Gallium and 10% of 1T of Silver - and your refinery slots are full. If you get a chunk that contains say 10% Silver and 10% Gold at this point, the gold has no refinery slot to go into, so you have to vent it.
I've crashed out to the main menu 3 times however. After 15 minutes and 3 asteroids, I had Bernditate and Endite (spelling, I know) in my refinery. My 2 refinery slots now contain Bern at 90% and Endite at 80%. Pick up a chunk of Bern and see that it also has Silver. I don't have any room in my refinery for silver, and since I'm so close to finishing up both my End and Burn, I figure I just vent the 10% of silver I picked up, and that way I have room in my hopper to finish up Bern and End.
Problem is, when I eject my Silver, server disconnects and back to the main menu I go. Happened 3 times in a row.
Not sure what multiple Mining lasers would offer you. Maybe twice the chunks, or 1 chunk shows up twice as fast. Either way, you're limited to the amount of flying skill you have to pick up the chunks - that's your bottleneck, not the mining laser speed. You can usually free up all 10 chunks with 2 charges of a single mining laser, which takes about 2 minutes or so.
Anyway, I'm fairly impressed with the system. Dynamic vistas and the orbiting asteroids plus the relative difficulty of picking up the chunks before they spin away too far is a challenge. Head out to a Styx asteroid site even if you don't have a mining laser and just check out the big rocks floating super close to the glare of a giant sun, it's really dramatic looking.
Didn't see anyone near me nor any pirates. Much like Exploring, it's not very exciting nor is it very profitable unless you get lucky picking an asteroid with expensive minerals. I found it to be relaxing and you have to concentrate just enough where it's not just SC'ing to distant stars so you can scan them. I'm in Styx like everyone else, and I don't think the asteroids "give crappier materials the more they're mined". I think it's more like "the easier they are to get to, the crappier the materials".