If the mining base includes a precursor item (the diamonds), you can add a module to "harvest" that as well as any special resources.
If you have the correct government types, the market tab becomes available and you can purchase the special resources for a fee. Of course, if you are mining them, you can also sell them there.
The AI's are much better now in building bases to obtain these, so building advanced scout is more critical if you want these. The production is much lower since Intrigue, so each mining base is more critical to success.