Credits are the currency

At the end of every week you get depending on confidence of every country relief which is payed in Credits. The confidence of other countries is calculated with Points, which you get for:

Finishing a research project
Shooting down UFOs
Attacking and looting crashed UFOs

Other methods to earn credits:

Selling equipment (you need Alphatron to build equipment in your workshop)
Fighting ground battles (50% of the Points you earn will be paid directly, the rest will be stored for your weekly balance)
Completing special missions from countries (depends on the game set)
with some technologies you can get a patent (you get some money for each patent you have)

How to loose credits:

Refuelling and repairing your aircrafts (done automatically)
Purchasing equipment and recruiting personnel
Building and maintaining structures and bases