There are a few Elite Mining guides and YT videos out there that will cover the basics (this one for example).
But the main thing that will help is there are two types of mining, and you need a slightly different setup for each.
The first is laser mining where you’re using your mining lasers to blast off chunks of minerals. The second is core mining where you’re planting charges into motherlode asteroids to blow them apart and get at the meaty goodness inside. If you want to maximize speed and profits, laser mining is where it’s at these days, but I prefer to core mine because I like blowing shit up (and it’s more interactive).
For each type of mining, you need to use a surface scanner on a ring (find one with pristine reserves, and hotspots that overlap on rings are definitely the best), then dive into the ring and proceed. If you’re laser mining you just need to use prospector limpets on any asteroid to find what you’re looking for, and then use your mining lasers on it and the goodies will chip off. Pick them up with collector limpets, and then use the refinery.
With core mining you have to pick and choose your asteroids, so you use the pulse wave scanner to look for motherlode asteroids. These have a slightly different look in the scanner, generally brighter yellow, and you’ll learn to recognise their distinctive shape after a while.
Then you can fire prospector limpets at it to see what it contains, and if that’s all good you use the seismic charge launcher to plant explosives in fissures and blow it apart, finally using the abrasion blaster to free the minerals, then use collector limpets and refine. Planting explosives takes some judgement so you get maximum yield.
You can set up the Asp to do both if you want, I’d try both and figure out which you prefer doing, and then install the most cargo racks you can manage and go for it. But really, there are great guides which will explain the nitty gritty details if you like.
Mining can be very profitable once you do it right. Making 20+ million credits in a session is not hard.