You build them on the node and it will double the resources from the resources associated with that node. E.g. 1 radioactive, or 3 metal etc.
So if you capture a node with 3 metal:
Capture node = +3 metal to income
Put extractors on metal resources: +3. Now a total of 6
Add poweramplifer: doubles resources so: 6x2 = a grand total of 12 from that node
That is how I believe it works.