Though other activities such as agent missions and pirate hunting are gaining popularity, mining is still the most common way for new pilots to make money in EVE. You can make the most of your intial training periods by mining as you're learning new skills. Simply select an asteroid field, head for the nearest lump of rock, target and let your mining laser do it's thing until your hold is full. Scoot to the nearest station, refine and sell. Cah-ching!
Occasionally, you may find an empty asteroid belt. This means that an industrious group has been there recently and strip mined the area. In time, the supply will be replenished. Try another belt or, if necessary, another system. Before traveling, you may want to check the map to be sure your chosen destination is safe and that a refining facility will be readily available.
Though you can lock onto targets from further away, you need to be within 10km of an asteroid to extract it’s ore. Use the "i" icon to get information about the various types of ore available in the belt, particuarly if you are looking for a certain type of mineral. This will show you what type of ore the rock is made of and what minerals it will yield.
Once your cargo hold is full, head back to the station. After docking, transfer your cargo to your hangar by clicking the "Items" icon at the bottom of your NeoCom, and drag the ore from your open Cargo window. Click the "Refine" icon in the Station panel. You will need a set amount of each ore before you can refine it for minerals. If you need more, return to the asteroid field and fill up again until you have enough.
Mining in groups can be a fun way to enjoy spending time with friends while making a tidy profit. If you are mining in a group and another player is shuttling the ore to the station for you, you can eject the cargo to make room for more ore. To do this, RIGHT-CLICK and select "Jettison" on the ore in your cargo hold, then drag the ore from your hold to the cargo canister as you mine it. (NOTE: There may be "ore thieves" in the area. If an unidentified ship comes within 1.5km of your unsecured canister, they remove its contents. Always be aware of who is in the neighborhood and take precautionary measures to protect your belongings.)
While pirate ships often hunt in asteroid fields where unarmed miners are grazing, in 0.9 and 1.0 systems you will probably be safe from attacks. Remember that the lower the security status of the system, the greater the income from mining the rarer asteroids found there and the greater the danger of ambushes by pirates who would rather fight than mine.
Once you have refined your ore, you can sell the minerals on the market. Click on the "Market" tab in the Station panel to check regional and local buy and sell prices. You can also RIGHT-CLICK on the newly refined minerals that are in your hangar (the "Items" icon in the NeoCom) by RIGHT-CLICKING and selecting "Quick Sell". (NOTE: Unscrupulous traders have been known to set low buy orders, so take a note of the current average price and don’t accept offers that are too low.)