Fortunately, there are many ways to figure out what ring size you are.
First, let's discuss how a ring should fit. Generally, it should fit around your finger without a great amount of tension. It should be snug enough not to fall right off while at the same time, leaving you able to slide it off without much trouble.
The most common ring sizes are from 5-7 for women and for men the average ring size can be anywhere from 8-14. The most popular sizes for women and for men are 6 and 9, respectively. With that said, these are generally good starting points when trying on rings if you're in the store.
It is extremely important to measure your ring size multiple times at different parts of the day to ensure it's accuracy. Your finger size can vary slightly depending on weather, time of day, and temperature. Fingers on your dominant side could very well be slightly larger.
Methods for determining ring size:
String and Paper Method
Needed items: pen/pencil, a rule, and a string or a piece of paper
Cut a string to three inches long.
Wrap it around your ring finger snuggly at the bottom of the knuckle.
Use your pen/pencil to mark where the ends of the string overlap/meet each other.
Measure the length in millimeters. Once you're done with that, look up what ring size corresponds to the given millimeter length.