Without cracking it, you can do a simple test by putting the egg in a bowl of water:
If it sinks, it is fresh. (Top right)
If it stands upright, it is a few days old. (Bottom right)
If it floats, it is rotten.
You should store the eggs broad end up pointy end down, in a cool place. It is not necessary to keep them in the fridge except in very hot weather. Stored like this they should keep for up to two weeks. If in any doubt just do the test described above.