You should be more specific when you say "Romans". If you mean ancient Romans, almost no mathematical text survived in Latin from the times before 2nd century AD.
From the Roman empire we mostly have Greek texts.
(See also Roman engineers). Almost all technical literature which we have from the Roman empire is written in Greek. Greek was also the spoken language of large portion of the empire.
Greek system is described in detail in the book of van der Waerden, Science awakening.
The digits of the decimal system were denoted by Greek letters. One had to memorize
(as we do) the multiplication table for digits. That's all one need to multiply numbers. For example,
To simplify the task, a counting board was used with counting stones.
Such a counting board in mentioned in Polybius, for example.
For computations with simple fractions a more complicated algorithm was used.
For astronomical computations, Babylonian positional system with base 60,
including fractions based on 1/60th was used (but the numbers from 1 to 60 were denoted by pairs of Greek letters). Multiplication tables were used (as Babylonians did before).