Your ring should fit snuggly on your finger without risk of falling off. Not too tight. Not too loose. You do not want to be hurting yourself or putting too much pressure on the ring or your finger getting it on and off. It should just be able to fit over the largest part of your finger which is often the knuckle for most people and bands approximately 6mm wide or more generally require a slightly larger size for most people.
Keeping this in mind; it is really important to check your ring size more than once which applies to both a simple home check or even a proper sizing in-store with a jeweller. Your fingers will swell in warmer weather and vice-versa in cold weather. This is particularly important for wedding and engagement rings as they will be worn everyday for a long period of time. Check your size on a cold day and again on a warmer day. Checking two or three times is not going too far because getting it right the first time could save you time, frustration and money on potentially expensive resizes.