Mining is the profession of extracting ore from asteroids, ice from ice fields and gas from gas clouds. These materials can then be refined into minerals, ice products and boosters. These refined substances are used in the production and maintenance of all player-created items and structures in EVE, such as ships and modules. It is one of the few professions immediately available to beginning players and most EVE industrialists started their careers by mining. Mining is perhaps the second most economically safe profession in EVE, save planetary interaction, in high-sec systems. Losing mining ships and/or being podded is uncommon and minerals are always in demand. Mining is accomplished by finding an asteroid belt, ice belt or gas cloud, and mining its asteroids/ice asteroids/gas clouds with special ship modules (mining lasers, ice harvesters, and gas cloud harvesters, respectively).
The basic mechanics of mining are very simple: Fit your ship with a mining module, approach and target an asteroid, and activate your mining module. At the end of each cycle (usually between 1 and 3 minutes, depending on the module used), the ore mined is automatically deposited in your ship's cargo or ore bay. The mining module will then automatically continue mining until either your cargo/ore bay is full, or the asteroid has been “mined out” (all the available ore in that asteroid has been mined and it disappears). Make sure that you keep the asteroid within range of your mining module (usually by stopping your ship, or orbiting the asteroid) - if you are too far away, the mining module will finish its current cycle regardless, but you will receive no ore.
If you're using mining drones, launch your drones once you are near the asteroid, and give them the command to “mine repeatedly”. They will then fly to the asteroid you have targeted, mine for one cycle (60 seconds), fly back to your ship, deposit the ore they have mined in your cargo or ore bay, then automatically fly back to the asteroid and continue mining it (until, as above, either your cargo/ore bay is full, or the asteroid has disappeared because it no longer contains any ore). Since the drones have to fly back and forth repeatedly between your ship and the asteroid, it's worth flying as close as possible to the asteroid to keep their travel time down to a minimum.
Once your cargo or ore bay is full, bring the ore you have mined to a station (either fly there yourself, or transfer the ore to another player's ship to fly back (see solo mining and cooperative mining for more details)), then return to the asteroids and continue mining!
There are three types of ships used in mining: a mining ship, a hauler and a mining support ship.
The skills needed for Mining can be basic and very advanced. For a list of relevant mining skills and their uses check here
Mining waste probability, which is a chance per cycle for resources to be turned into space dust.
Mining waste is taken from the asteroid and not from the mining yield.
There are a number of mining strategies used for both solo miners and cooperative mining.