I'm not interested in creating a step-by-step mining guide for a first-day player. Instead, I'll focus on how I mine because that's what gives me a great deal of satisfaction. Having done it for a couple of years, those new to mining, especially those new to small fleet mining, may find a few tips that help them enjoy the activity a bit more.
Miner: The pilot who extracts ore from asteroids.
Booster: There are skills, ships, modules and an implant that will increase the efficiency of your miners. My booster flies an Orca as all of my mining is done in highsec. I will discuss the Orca and the Orca pilot at some other point. I won't mine without a booster.
Hauler: I don't like jet can mining, warping to stations to empty my ore hold or trading off the yield of the Hulk or Covetor for a larger ore hold. Instead, I use a combo of the Orca and a freighter (Charon) in the field so my miners can continue to do their thing until the belt is cleared of the ores I'm after. Miner-Orca-Freighter is one field combo. There are others I'll discuss later. Your hauler will also be used to transport your ore, minerals or finished products to market.
Refiner: The ore you extract from asteroids can be sold as ore or can be refined into minerals and then either sold on the market or put to use in the manufacture of items. The goal of each step subsequent to ore extraction is the adding of value - minerals worth more than ore and manufactured items worth more than their component minerals. That's the idea at least - value added. However, adding value to ore through this chain requires a decent amount of market knowledge and perhaps a trader.
Trader: Whether you sell the ore, the refined minerals, or manufactured items, some selling will take place. If you mine/refine/manufacture in significant quantity you won't want to give away your margin to poor trading.
Inventor/Manufacturer: You mined ore. You refined the ore and received minerals. Now, if you choose, you can take those minerals and use them as components in the manufacturing process. The key point is that each step of this process - refining to manufacturing - should add value to the mined ore.
T1 Mining Vessels and their T2 Counterparts
Venture/Prospect (frigate-sized miner) (solo)
Procurer/Skiff (tank) (solo/fleet)
Retriever/Mackinaw (cargo hold) (solo)
Covetor/Hulk (yield) (fleet)
Of course, the big question is, what ship should I use/train for?
And of course, this being Eve, the answer is: it depends. Each ship has its purpose and there are situations in which it is probably more appropriate than the alternatives. I'll discuss this in more detail as we go along. I made a note of whether the ship is used primarily solo, in fleet, or both, but that doesn't mean you couldn't use a Retriever/Mackinaw in a fleet, etc., it's simply my opinion as to the ship's primary use.
Capital Industrial Ships
I will have much to say about the Orca and the Orca pilot as I use it every day in highsec mining. If I mined every day in low or null, I'd use the Rorqual. For now, I'll just say that their primary service to the miner is boosting mining efficiency through the use of Mining Foreman Link modules.
To haul ore off a mining field, the two basic choices are the Miasmos (Gallente T1 Industrial) and the freighter. The Miasma is a relatively inexpensive T1 hauler bonused for the amount of ore it can hold. The freighter is a capital class ship with an enormous cargohold and an enormous pricetag.