In part 1 we discussed the two principal methods of mining along with some criteria you might consider in choosing between the two methods. In part 2 we'll discuss some general techniques one should use in mining. I assume, for the sake of this article, that you are mining in a high-sec sector, and so won't cover ship fits that you most likely would want to use in low-sec mining.
If you are interested in mining as a long term money making operation, and plan on mining for longer than an hour or so at a time you will probably want to establish a mining route for yourself. In whatever system you like to hang out in, or would like to mine, right click out on empty space and mouse down to the Asteroid Belt menu. That menu will display all the available Asteroid belts in the system. Before beginning your mining tour I suggest you jump to each of the systems in turn and bookmark two or three asteroids in the belt. It isn't unusual for a warp point for the belt to be a considerable distance from the belt itself, and it is a waste of time to warp into the warp point, and then have to motor into the asteroids every time you visit. If you solo mine without jettisoning then you will be doing that quite a bit. If you bookmark several asteroids in the belt you can simply warp directly to that spot in space the next time you return. When making your bookmarks try to make one for the middle of the belt, as well as one on the extremes of it as well. That way you can choose to warp to whichever point along the belt you want to return to next trip and minimize the amount of time you will have to take to travel along the belt to get to particular asteroids. Asteroids will disappear as they are mined for all their ore, so being able to jump into specific parts of a belt saves a lot of time.
Once you get all your bookmarks made you can simply start at one end of your route and work your way through it. Depending on the time of day and the system in question, you can probably mine for a good period of time without seeing anyone else at all. Or very few in any regard. Less competition means more ore for you, and that is the reason for making a route to begin with. As the asteroids are mined you can simply move along the belt until they are all gone, and then move along to the next point in your route.
And as you are beginning your mining and are probably looking at different types of asteroids, you should be asking yourself which do you want to give preference over others in mining? First you need to know what types of ore can be found in which zones. Check out the "roid grid". If you are a beginning player the chances are that you are in 1.0 or .9 space so you will most likely only be seeing Veldspar or Scordite. Whatever you mine you will notice that some asteroids are regular (i.e. asteroid (veldspar)), or condensed (i.e. asteroid (condensed veldspar)), or dense (i.e. asteroid (dense veldspar)). The differences between these three variants is in the amount of refined mineral they will give you when refined. Condensed asteroids will give you +5% yield, and Dense asteroids will give you +10% yield, so you obviously want to give preference to Dense, then Condensed asteroids when mining. I'll move along an entire belt mining only the Dense and Condensed asteroids before I mine the regular ones. Time equals money after all. Check out the ore guide for what minerals refine from which ores.
If you find all of the belts you normally mine are mined out another option for mining in that system is to run missions. You will normally find asteroids in the dead space zones where missions are run. Deal with the pirates (or whatever) and then find the asteroids. If you are going to attempt this, you obviously need to have some means of protecting yourself. Make sure you either have enough weapons equipped on your ship to deal with pirates, or make sure you can carry drones. If you are capable of carrying at least one drone, make sure it is the best combat drone you can handle. The better your drone skills, the better your drone will be, so don't neglect those if you intend to do this. You say you can't find any asteroids? Learn how to use your on board scanner (ctrl-f11). I use a residual survey scanner myself. In fact equipping one of those might be a good idea under normal circumstances because it will tell you which asteroids have the most ore in them.
If you are in a ship that is capable of handling two or more mining units you'll want to make sure you mine as many asteroids as you can at a time. Initially you will only be able to lock onto two asteroids, but if you train in Multi-tasking you can increase the number of objects you can target, up to the limit of the ship you are in. If your ship can carry two mining lasers then target two asteroids and assign a mining laser to each. You do this by targeting one, clicking on it after it's been targeted and then turning one of your mining lasers on. Rinse and repeat with the second mining laser. While you are a beginning miner it isn't important enough to train multitasking over other important skills. Add it in, if you feel like as some point, if you feel so inclined.
Lastly, if you are solo mining. Which means you will be mining and hauling your own ore into a station. And it also means you are probably planning on refining your own ore. If you are, it is very important that you increase your refining skills. The lower your refining skills, the more ore that will be lost in the process. Of course your security standing with the station you are refining at counts in this equation too. Regardless of anything else, work your refining skills in as early into your training plan as possible, and work on your security status with the station when you aren't mining.