Most of the foal's time will be spent napping, nursing and playing. As much as possible foals should spend time outside with other mares and foals. Occasionally you might see a foal sampling a pile of manure. This is natural and will not harm the foal.
Foals should not be allowed to nibble on people, strike out, or kick. While these behaviors may be cute in a small foal, they can become dangerous as the youngster gains size, strength and speed.
Foals should learn early to have their feet handled, especially if corrective trimming may be needed. This is done by holding the foot up for a few seconds and putting it down again. As the foal learns to accept the handling and learns to balance, the length of time can be increased.
A small foal halter can be put on, but it can be a hazard to leave it on if you're not present. Foals often scratch their ears and face with a back hoof and a hoof can get caught in the halter. Foals can stick their heads through gaps in fencing or stall walls that a larger horse wouldn't, catching the halter and becoming entangled.
Lessons in leading can begin and a foal should learn to walk quietly beside the handler. I do not like the idea of tying a foal. This lesson can be learned a bit later in life and then taken slowly and sensibly so there is little chance of the animal panicking and hurting itself.