Because I wanted to know if I have been making a mistake by tring to mine at places that don't have a suitable quality of resources, I set up for mining last night despite I didn't want to play until Odessey has been released. I have always found that hotspots have, if any, only trace amounts of the mineral the hotspot is indicting, which makes mining totally broken. Last I time I had to mine, it took me about 6 hours to get the 10t Painite for an engineer. Other players seem to be having the same experience while yet others seem to be happyly mining hundreds of tons of minerals within an hour or two.
Perhaps I have made a mistake or not (or lots of mistakes); it has been bugging me enough that I decided to find out. So last night I set up for mining and entered a Musgravite hotspot in a ring in Silikians. The gas giant the ring is around shows as pristine resources. I didn't have much time left and could only do a short survey, and I found the usual picture: There was a single asteroid having a Musgravite core --- which surprised me because they are so rare --- and a bunch of other asteroids that had various kinds of minerals none of which are precious.
Lot of useful answers already, but lets get a bit back to the basics
Laser mining.
You need A-rated prospectors, Collectors (the more the merrier), 2 medium mining lasers, enough storage, refinery, DSS and not at last limpets. Lots of them limpets, like 60-80% of your total cargo capacity
Lets say you want to go painite mining:
According to
miners tool you should go to a system with an overlapped double hotspot (Hyades Sector DB-X d1-112 , planet 2 , ring A), scan the ring with the DSS then drop in the middle of the overlapped painite double hotspot. Then you set a general direction and fire prospectors to any asteroid you see.
If it has paininte, more than 20% as prime material, you mine it etc. IF needed abandon some limpets to make room for painite. When full go to a station and sell
Deep Core mining.
You need the same as above with the following differences: no need for mining lasers, you replace them with abrasion laser and seismic charge launcher, you also need PWS (A rated preferably)
You find a preferred material (but make sure you avoid ice rings - they were badly killed in July) and go to a Hotspot.
Now, for core mining, the hotspot will increase the chance of getting cores for that material. You will still get other cores for other materials present in the ring and rng can be nasty.
So again - the hotspot will not increase the number of cores, but the chance that those cores will contain the hotspot material. Even so, bad rng can ruin your day. I remember getting 5 bromellite cores in a row, followed by an alexandrite core in an Void Opal Hotspot.

- obviously that was back in the days were Ice rings were ok.
A double hotspot for that type of material will increase the chance even more so you'll likely find mostly cores of the hotspot material
A triple hotspot will basically guarantee you will get only cores from the hotspot material.
The cores are usually rather far between - on average you'll get a core every 50 km (for sure the rng can make it so you will find 2 cores within 5km of each other, but that is very rare). So you need a ship that can boost fast and often and of course use the required tricks to make that bugged PWS work.
Once you spot an asteroid that might look like a core - send a prospector, etc... you know the drill (pun intended)
I forgot to add - cores are persistent in the ring. An exploded core will be visible between modes and it will stay cracked for days - i think a full week? - until it regenerates
As a comparison - a laser mined asteroid will replenish its content in 2 hours. Laser mined asteroids are not persistent between modes. 10 people can mine the same asteroid, each in his own Solo mode / instance - without any issues for the other miners.