Your feet swell when you run, so you should be wearing running shoes that are a half size to a full size bigger than your street shoe size. If you have a wide foot, you may need to get a running shoe that has an extra-wide toebox. You can ask a salesperson at a running specialty store for advice on the right shoes.
If you think your shoes are the right size, you can also try stopping to stretch when you start feeling the numbness. Sometimes tightness in our legs may lead us to run with improper form, which may put pressure on a nerve and lead to the numbness. So a quick stretch of any part that feels tight may help. When you stop to stretch, also try to move your foot around and massage it a little, just to get the blood flowing to the areas that feel numb. Running on your toes for 30 seconds or so can also help.
If you don't see any improvement with the above advice, it's important that you see your primary doctor or a podiatrist. You may have a nerve issue called a neuroma. Though it may sound scary, a doctor-recommended under-the-foot pad can help treat the condition by taking pressure off the nerve.
The numbness may also be the result of something more, like an illness, tumor or nerve condition. If your symptoms persist, don't wait to get checked out.