You'll pick this up by trying. Most of the time you will need more than one layer of a colour for a good coat. Let it dry before putting on the next layer.
Only use the tip of your brush, don't let the paint run up to the metal part. This will ruin your bursh as it will dry between the hairs, destroying the tip.
Get a decent brush. If you painted a couple of mini's and know you'll continue, it is probably wise to invest in an expensive brush such as the fabled Windsor and Newton 7 series (~€12 were I live), as it really helps with painting, but if you're just starting out you can get cheaper ones made by miniature companies such as army painter of GW.
Are you painting boardgame models? Most of them are of a soft type of plastic, and have some kind of residue on it from the production process. This will prevent your paint from sticking to the miniature. Wash them in soapy water with a toothbrush, let them dry, and undercoat them. I prefer a spray can, you can buy expensive ones from games workshop or other miniature companies, but cheaper ones work as well.
Expensive miniature paint is expensive because there is a lot of pigment in it (compared to other types of paint). You don't use it straight out of the pot, but dilute it with water on a dish or something. It covers far better than other types of paint in my experience. and a small bottle goes a long way. I don't see how you can save money by buying paint that's cheaper volume-wise, volume is not a limiting factor. I have experience with Vallejo Model range (mainly military colours and such, a lot of pigment and needs a lot of thinning), Vallejo model range (a bit thinner, wider range of saturated colours mimicking that of a big miniature company) and Games Workshop paints. Vallejo is cheaper where I live, and comes in better bottles so I usually go for those.