Depending on the type of bird, many experienced breeders can tell whether an egg is fertile or not around the 3rd to 5th day after laying.
While the parent(s) leaves the nest for a while, with a gloved hand, preferably a clean, white cloth glove or non-latex rubber glove, hold the egg just up enough to shine a flashlight from behind it.
If you see a dark spot in the middle of the egg, slightly off center and a spider web of small red veins around this spot – fertile.
The gloved hands are not so the parent doesn’t smell you on the egg and reject it, it’s to protect the developing embryo from the natural oils and bacteria on our hands. The eggshell, though pretty solid feeling, is extremely porous.
Keep this in mind and remember that not all fertilized eggs will hatch. If a parent is carrying a bacteria, virus or parasite – even though they might not show symptoms whatsoever – it can be passed on to the chick and result in a dead egg at some point in development.
This is also what is usually behind ‘failure to thrive’ with baby birds that hatch, but don’t make it beyond a certain point (usually a few weeks) after that. For this reason, before undertaking a breeding, parents should be thoroughly checked and given a clean bill of health which also includes a DNA/genetic screening.
UC Davis has a very good visual guide to help determine egg fertilization (or not)
UC Davis Candling Guide