The Romans hadn't indian numerals, but what 's worse hadn't the decimal system, yet produced amazing works of engineering and architecture. How was that possible? It's troublesome to make simple sums, but how could they make products and complex calcs? Any textbook of math survived to tell us how they made complex calcs?
They used abacus. The techniques used for operations with abacus were understood and were basically the same used also until quite recent time also in China and Japan, as far as I know. This does not require indoarabic numerals.
In fact you shouldn't think "Latins". Latin numerals were in use in Europe till the XIIIth century at least.
Liber Abaci by Leonardo Fibonacci is credited as being one of the main sources of introduction of indo-arabic numerals in the Western countries and dates back to 1228. One of the reason of its success is exactly that it explained how using such numerals could improve computations. It is, in fact, a Book of Abacus, as the name says, i.e. a book centered around techniques for algebraic computations.
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, $$265\times265=200\times200+200\times60+200\times5+60\times200+60\times60$$ $$+60\times5+5\times200+5\times60+5\times5=70225.$$ 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).