|Very fresh eggs sit at the bottom.|
|Older, but still fresh, eggs rise up on one end.|
First, it's important to realize chicken eggs last a long time. In fact, the eggs you buy in the grocery store are, well, old. It's difficult to know exactly how old. Some source say several weeks; others say 6 months. According to Life Tips (who quotes the American Egg Board), store bought eggs are safe to eat 4 to 5 weeks beyond the packaging date. That lines up with my personal experience.
I've also personally kept backyard eggs refrigerated for several months with no problems at all; just be sure to wash the eggs before you eat them - not before you store them. (Chicken eggs have a natural barrier on the outside that prevent bacteria and other germs for penetrating the shell. Washing removes that barrier.)
Second, learn this simple rule: As eggs age, more air enters their shells. How do you know how much air has penetrated an egg shell?
1. Place the egg in a glass bowl or large glass measuring cup filled with water.
2. If the egg sinks, it's quite fresh. If just part of the egg floats upward, it's still good. If the egg floats to the top, it's bad.
Here's a great visual to print out as reference - but just remembering that the airiest (oldest) eggs will float makes this simple test easy to remember.