Those are called "Trexler Air Wheels" or "Balloon Wheels".

After you inflate them, twist the inlet tubes a couple of turns and tuck them under the wooden hubs. You can work them around under the hub until they are almost completely hidden between the hub and the tire. This will hold the pressure in the tire.

You should not use your breath to inflate the tires (though I always did, against Trexler's recommendations) as the moisture in your breath will cause the inlet tubes to stick together (internally). Then it takes a lot of work to get them unstuck so you can get the air out. If you find this to be a problem, try twisting and stretching the tubes and eventually they will open up, but they can be a pain.

While I like the looks of the Trexler Air Wheels, they never seemed to be very durable. They seemed to get a lot of "flats" caused by the tiniest sharp objects (almost microscopic) causing punctures.