Severe lack of mining tips on here so here's a couple (Lost track of the numbers so just pop in as appropriate). I appreciate mining isn't a newbie job, but I see it as more "Newbie Miner" tips:
Look for Metallic Rings AND Pristine reserves. Anything else is pretty much worthless owing to the rarity of high profit materials. Once found, STEER CLEAR of RES Sites as these are often (if not always) populated with pirates. Just find the ring and approach the metallic (grey/silver) parts at safe speed, you will drop out the same way as when you get too close to a planet/star.
A Refinery is necessary. You cannot mine without it, as there is no storing unrefined fragments. If you cannot fit one with at least 4 bins, you will spend A LOT of time staring at the systems panel venting worthless materials. Similarly, do not fit a Class 4 Refinery if that's most of your cargo space gone. You may spend less time venting, but you will spend more time travelling than you will mining, which will seriousky hurt how much credits you earn.
Collector Limpets speed up the mining process considerably but require a Collector Limpet Controller which reduces your maximum cargo capacity. Balancing the size of your control module vs the speed which you mine fragments.
-to clarify, with class 1 mining lasers there is absolutely no need to have 3 or 4 collector limpets out at once, so equip a smaller control module. Conversely, if you have Class 2 mining lasers, 1 limpet will have you waiting ages to finish collecting the fragments even AFTER the asteroid is depleted.
Prospector Limpets are COMPLETELY optional, and perhaps not recommended for smaller ships as, once again, they require a seperate control module in your internal compartments, (i.e. Prospector Limpet Controller). However there is a hidden bonus to using them besides getting a read on the composition of the asateroid. Prospected asteroids will net you twice as many fragments as the same asteroid without prospecting. (If an asteroid would normally give you ten fragments, prospecting it will give you 20).
The most worthwhile materials to mine for are Palladium, Platinum and Painite, more commonly referred to as the "three P's", but Gold is a viable alternative and there are frequently bulletin board missions asking for Osmium at a rate of 50-100k per ton. The more cargo you can hold, the less fussy you can afford to be. For example, mining in a cobra should be dedicated to only the three P's where possible. However in a Python or Anaconda, just blast every rock and ditch cheaper stuff or limpets to make room for more profitable materials as required. (Personal note: I find that if you spend less than one hour mining between trips to and from the station(s), you are either VERY lucky, or not being fussy enough with what you collect)
Do not hesitate to dump your limpets no matter what you are mining. Limpets are ~100cr per ton. There is nothing you can mine that will earn you less. If you are returning to the station with half your cargo filled with limpets, you're doing it wrong. In addition to this, don't leave the station full to the brim with limpets either, you will be dumping them constantly. Start by leaving 3/4 or 2/3 of your cargo empty, and adjust accordingly if you are running out before you are full, or dumping loads of them.
I have plenty more, but this is probably enough to get you started at least.