You just have to explore quickly and find a few bodies with good sources of minerals. I tend to count the total availability of all minerals on a body to determine if I want to put a mining colony there. For example, if there are 4 minerals on it in decent amounts with availabilities of .4 .8 .9 and .7, I'd add it all together and say it's 2.8, which is decent but not great. I try to look for bodies with a total of 3 or more and at least 100k of each mineral it has.
If a body is unsuitable for colonization, I use freighters to ship automated mines to it and put a civilian administrator with a good mining bonus in charge. If it is suitable, I ship some infrastructure to them and then a bunch of regular mines. I use mass drivers to send the mined minerals back to my homeworld, or just put a freighter on a cycle loop of picking up the minerals from my various mining bases. You don't need a ton on infrastructure on a new world for it to support enough civilians to be a valuable mining colony (a few hundred units will do), and your civilian shipping lines will bring more infrastructure to it automatically as trade goods to let it grow on its own.
Anyway, that's my approach. You may find another way works better for you.
