1) you found them with a Great Person.
2) Corps don't consume resources...if it uses copper, for example, you can still use copper in any other cities. Keep in mind that the amount matters. If a corp uses, say, rice, wheat, and pigs, then 3 rice is the basically the same.
3) apply Solver's patch, it fixes a bug in the corps. Personally I changed an .xml file to better balance corps (at the recommendation of Solver). Regardless, most corps aren't great money makers. Even if you found the corp in a Wall Street city with banks and such, you wont make a huge amount (even without the change that I did). To make great money with corps, you spread them to foreign nations.
However, keep in mind that applies whatever bonus the corp gives to their cities. Mali hastened my Space Race victory in my last game by spreading Mining Inc to me
4) Build COURTHOUSES. This is important. Corps cost a crapload in maintenance.
the nation?) -- which is useful, should I have 2 of a resource and none of another? I assume each corporation changes different resources?
No. ONE corporation will consume some resources and give you aluminum, and another will do the same for oil (and give you some extra beakers too). However, each corp has different effects. Creative Constructions, for example, gives the target city extra hammers and culture. Also, as stated above, you wouldn't lose access to coal if you used it for a corporation.