The Cubit is the standardized currency of the Twelve Colonies and from all appearances the only currency in existence.
There is unfortunately no value easily equated to a cubit (e.g. 1 cubit = 5 USD)
Coins[]
Coins presumably represent the smallest denominations of cubits and come in both gold and silver. Like many things in BSG, these coins are octagonal in shape. On the coin's obverse is the symbol of it colony of origin. On the reverse is the colonial insignia. In this way, cubits very much mirror the Euro and the ideas of Colonial Unification through a shared currency.
Paper[]
For larger denominations, paper notes are used. Like the coins, the notes are fairly uniform but simultaneously have their own unique features to mark their colony of origin. Denominations include at least a 100, 500, and 1000 cubit note. Unlike coins (and most forms of BSG paper), paper cubits are perfectly square (or close to it).
Electronic[]
It can safely be assumed that the Colonies are not dependent solely on tangible currency and notes of debt. Thus cubits are also stored and tracked electronically through a modern credit/debit system. Such a system, like the very value of cubits, was likely thrown into turmoil during the Fall but it is likely that such a system has been somewhat salvaged or perhaps merely restarted in the Fleet.
