Good question :)
From the ground, some simple ways to tell if a horse is on the forehand are:
1. The croup is higher than the wither.
2. The front legs land before the hind legs.
3. The horse appears to be 'dragging' itself as oposed to 'pushing' itself.
4. Generally it is stiff, little bend through the body and will hollow its back and brace its neck when it turns or does a transition.
5. The hind hoof prints will not land in the front hoof prints - aka the horse is not 'tracking up'. Ideally you want the horse to overtrack.
6. The hocks appear straight and stiff. A horse that is carrying behind will bend the hocks and lower its haunches.
1. Often the horse will be either very lazy and behind your leg (doesn't react immediately to your driving aids), or will run through your aids (appears to be 'forward' but is actually just running along, still technically behind your aids as it won't react positively to the aid)
2. You will find that the horse does not react to seat aids, and you will end up having to pull on the reins to stop or turn the horse.
3. The horse feels unbalanced, you have to work to keep yourself balanced in the saddle.
4. The horse will be stiff - you will struggle to move the horse's body, it will not bend through turns or on circles, its neck will be straight and often its body will be crooked - i.e. quarters in or out, shoulder falling in or out
5. Riding the horse is not terribly pleasureable, you are forever working and trying to stay balanced.
A horse that works off the forehand is a delight to ride. It carries you willingly forward and is 'in front' of your leg, you apply the aid and the horse reacts immediately. You will get a feeling that you are able to move any part of the horse anywhere that you want - move the jaw a few cms to the left, a few cms to the right, move the shoulders across slightly, bring the quarters in slightly etc.
Its back will swing, making it easier for your to sit on and you will feel as though the horse is a coiled spring ready to react as you ask.
This is a fairly simplified explanation, I could go into detailed dressage terminology and explanations, but I suspect that is not what you are asking at this point :)