On this page of the guide to the Dyson Sphere Program you will find information on resource extraction. You will learn how to locate them from here.
The most basic unit for mining is the mine (mining machine). It is a multipurpose building that allows the extraction of raw materials from veins. All you have to do is place it next to one of the deposits and mining will start automatically. These types of buildings have limited storage space and you must connect them by conveyor belt to an industrial plant or warehouse to keep production running.
On the starting planet, you will find 4 resources that you can exploit with the help of the mining machine - copper, iron, stone, and coal. The rest (like titanium and silicon) appear only in residual forms in lying rocks. However, you have to keep in mind that you won't always obtain them, and the number of boulders is limited. Therefore, exploration to further planets is required.
You must also keep in mind that resource deposits are not unlimited - each vein you exploit slowly depletes. You can see their status by hovering the mouse cursor over them.
Another type of material you will be extracting is Crude Oil. You can acquire it by putting up an oil refinery. In this case, however, there is no question of resource constraints. What is defined is the speed at which the raw material is extracted - the higher it is, the faster the process will take place.