Me and my wife just moved in to her Aunts old house. We removed the carpet from on of the bedrooms and found then to be in good condition. There are dirt stains from the padding on the high traffic areas. The house was built in the 50's and I asume that is how old the hardwood would be.

What is the best way to remove these?

Depends on if the marks are caused by moisture or just wear into the finish. Any chance you can e-mail a picture to me? Very close up ...Click below on my e-mail and I'll send you my actual address to help.

Can't send a pic, but I don't belive it is caused by moisture. I can use my finger nail to scratch it and is appears to come off. When I first removed the carpet and padding, I used a soft brush a water to remove the top layer of dirt. Any ideas?

You Might try some mineral spirits. It's fairly mild for a solvent.
Whatever you do don't use anything like "Goo-Gone". Mineral spirits should
be able to clean the floor and not hurt your finish.If there is wax or
shellac on the floor Mineral Spirits will loosen them up. Try a closet spot
first to make sure that it doesn't cause anything to 'gum up'. T-shirt mat'l
works great. Don't pour it directly on the floor. Put it on the rag first
then wipe the floor with it.

Hope it works!
Good Luck,
William