Using it is really simple. On buses, you just need to bring it near the entrance reader and it will detect it. When you get down the bus, do the same, it will then calculate how much the cost is and deduct your card accordingly.
You can also use the card on the train system. Well, this card also feeds you! Yes, you can pay for your burger at McDonalds too.
Here's the picture of the card. There are new designs now, this is the old design.

Do you have such public transport payment card in your country?