In Federal prison it is common to use books of stamps as currency. When I was there (95-99) it was around $5 per book of stamps. But it was more common to just give someone a commissary list (for the prison store) of items totaling the amount that they owe you.

For larger amounts, you'd have to have someone on the outside send money to the other person's people on the outside. These days, I suspect Bitcoin makes this much more efficient (for transfers happening outside the prison).