People in ancient Greece had a variety of different ways of writing down numbers, but none of them was very efficient. (And of course different Greek city-states used somewhat different systems, too).
Some Greeks used a system based on writing the first letter of the word for that number. Like in Greek you say Ten “Deka”, so they would draw a D to mean 10. (A delta, actually, in the Greek alphabet). In this system though,1 was just written with a vertical line, like our 1 today. They used P for Pente (five), D for deka (ten), H for Hekaton (100), X for Xhilioi (1000), and M for Murioi (10,000). So you could write 539 as HHHHHDDDPIIII. But this was pretty hard to read.
To make it a little easier, Greek writers also combined these symbols to make special symbols for 50, 500, 5000, and 50,000.
The Greeks also used another system where the letters of the Greek alphabet each stood for a number, so 1 was alpha (A), 2 was beta (B), 3 was gamma (G) and so forth. (The letters in the Greek alphabet were not in exactly the same order as in English).
They did this for the first ten letters, and then the 11th letter stood for 20, the 12th letter stood for 30, the 13th letter stood for 40, and so on. After 100 the next letter stood for 200 and so forth. This system was more efficient to write. For larger numbers people drew a line over or under or next to the alpha to mean a thousand, or whatever, or over the beta to mean 2000.
But none of these systems was any good for adding or multiplying long strings of numbers, like if you wanted to keep accounts in a store. For that, the number system of India (invented around 600 AD) was much better – the system we use today is based on that. Nowadays we only use Greek numbers, or Greek letters, to symbolize an unknown in algebra.
Learn by doing: try to write some numbers in Greek numbers
More about Roman numbers
Can You Count in Greek – Exploring Ancient Number Systems, by Judy Leimbach (1990). Includes the Roman, Babylonian, Egyptian and Mayan number systems too, with lots of math activities for kids.