With the exception of doing the prison jobs the only other way you can earn money is by doing favors for other inmates. A prisoner who is after a favor (offering a quest) is marked by a green '!' (exclamation mark) above their head.
The type of things other inmates want done varies and can for example involve retrieving something from a certain inmates desk without being caught or fighting other inmates and guards in order to retrieve an item from them. Whatever the quest, once it has been completed you will automatically be paid. Note: You do not need a free item slot for these quests.