Cut feet are a very common issue with dogs out exercising, broken glass on the pavement or at the bottom of ponds or streams being a common cause.

If the wound is shallow and if any bleeding can be easily controlled by applying some pressure for a short while then it is unlikely that the wound would require stitches so may well be managed with home care.

In the first few days it is wise to cover the wound when the dog is out exercising, you can buy dog boots online or in some pet stores but a sock covered with a sturdy plastic bag will suffice. If you are putting a sock or other material over the foot do not tie it on tightly or you may hinder blood supply to the foot which can cause serious tissue damage, sellotape or insulation tape or similar will be quite effective for a short time.

So long as the wound is not bleeding it is best left uncovered as much as possible, fresh air is good for reducing the risk of infection.

Shallow wounds should be cleaned regularly (2 or 3 times daily) with salty water 

Dogs will want to lick a new wound and so long as this is not making the area sore it will not do any harm, if the licking is excessive and the area appears sore or swollen you should see your vet to check for infection and they may provide you with something to prevent excessive licking. 

Dogs with shallow clean wounds should not be in significant pain and so should not be very lame, it is important if they are getting increasingly lame that you see your vet as this would suggest infection and might indicate there is something in the wound (this we would call a penetrating foreign body)

Uncomplicated superficial wounds will usually be dry, painless and well on the way to full healing in 10-14 days.