Evidence, particularly from the Imperial Roman world, comes from archaeology and ancient writers. Archaeological evidence comes from tombs, mosaics, and tesserae (dice), which last show finger symbols on one side and Roman numerals on the other.
Burma P. Williams and Richard S. Williams, in their article "Finger Numbers in the Roman World and the Early Middle Ages," from Isis, Vol. 86, No. 4 (Dec. 1995), pp. 587-608, state that Quintilian said an orator would be considered uneducated were he hesitant in calculating or used the wrong gestures with his fingers while making a calculation. This shows that fingers were probably not just used to show numbers, but to perform operations like addition and subtraction on them. However, as the authors state, we don't know whether the ancients used their fingers merely to keep track of intermediate stages while making mental calculations or whether they used their fingers to actually perform the computations.
This finger number system appears to have been in used throughout the Greco-Roman world and well into the Middle Ages. That the Greeks used fingers for computations seems to be implicit in the Homeric term for counting, pempathai, which means to count by fives.
The article mentions a riddle (from Symphosius and Alcuin) which seems to show something about how counting was done: How can 7 from 8 equal 6? Since the number 8 was represented by lowering the little and ring finger of the left hand and the number 7 was represented by lowering just the little finger, if you start with the 8 -- i.e., little and ring finger lowered -- and then raise the little finger to subtract the 7, the ring finger remains lowered and that was the symbol for 6. Obviously, the wrong answer, but perhaps a cautionary tale for those learning the finger calculator.
