I keep dying from breathing the air!

You have to act fast in this part or you'll die from inhaling too much air.
If you run out of time, restore the game and try to do things faster.

You need a gas mask.

There is no such item in the game, but you can make one.

You need 4 items: a strap, a container, a filter, and something to make a
few holes in that container.

If you look carefully through the prescription book, you'll find a
suggestion or two about how to make the filter.

The smithie left town, but he left a few of his items behind.

Go to the smithie's shop, on the far left of Main Street.  Pick up some
charcoal and the leather strap on the wall.

A tin can would make a great container.

One can be found in Mom's Cafe, in the foreground.

You also need to make a few holes in the tin can.