To mine resources you have to click on the Research room, and use the tech tree to research it. Its in the first group of Tier 1 research after you start the project in the tech tree.
After that, you have to build a tunnel to the first square of a resource, then put the mine over it. Mines are only 3 long, and each square has more or less resources on it.
If you highlight the square it will tell you how much is in it, and give you an idea if its worth it to mine that one, or find a better one.