Yes, you can use clintz to buy character from other players on the Market. (just on the left side)
You can earn clintz by: playing, participating in any (or all) of the 3 tournaments we run each day, buying them at the shop
using credit, selling you characters (provided you have at least buy credit once with your account).
You can also buy new characters at the shop using credits that you can get with money (phone, text message if supported
in your country, credit card or paypal otherwise).