Remove the tire and rim from the front of the wheel barrow. This is a tube type tire so I used patches designed for bicycle inner tubes. For a few dollars you can buy a kit that has patches and glue. They should be available at any outlet that sells bicycle tires. There are some better patches available at auto parts stores but they're overkill for something that goes as slow as a wheel barrow!
Remove the valve core (it's threaded so just unscrew it) from the valve stem. Even though they seem flat, many tires still have residual air left in the tube. That makes it more difficult to remove the tube when the time comes. Taking the valve core out lets the last of the air out also.
Operation complete! The valve core has been removed! The tool for removing the valve core can be purchased at any auto parts store.
Squeeze the tire near the rim. The bead should easily come loose from the rim. Now pry one side of the tire off the rim. They make special tools for doing this but I usually use whatever is handy. In this case it was the wrenches I used to remove the wheel assembly. A couple of large screwdrivers will work too. Be careful that you do not tear the tube with the tool you use to pry the tire's bead from the rim. Start at any point by inserting your tool under the bead on the tire and prying it over the rim. Leave your tool in place to hold the bead over the rim. Insert another pry tool a few inches from the first and pry the bead over the rim again. At this point you can remove one tool and work your way around the rim until one side of the tire is free.
Once you have one side off reach in and remove the tube. Now you'll need to pump it up (our grandson volunteered for that job!) to find the air leak. Put just enough air in to find the hole. With very small holes you may need to put the tube under water and watch for bubbles.
This tube has scuff marks where the tube has been pinched at some point in the past. You can see a previous patch to the left of the circle.
The patch kit I have had a large patch that you could cut to the shape you need. I cut a long patch to cover the scuffed area.
Be sure the tube is clean before applying the glue. It helps to rough up the surface a little bit too. Many tube kits have small metal tabs with a rough side for doing this. Coarse sandpaper (my favorite) will work too.
Next take some glue (the rubber cement that came with the patch kit) and apply it to the area needing patched. Be sure to make it large enough so that the patch will have glue under it's entire area. I usually put a few drops on the inner tube then spread it with my finger. I put it on a little thicker than necessary in this photo.
The patch will have glue on one side. There's a protective plastic covering (blue in this instance) you'll have to peel back before putting the patch on.
Once the glue has dried apply the patch. The tool I'm using has little serrated wheels that press the patch down into the glue. It's available at any auto parts store. A golf ball works well too as will any hard object you can "roll" over the patch. Press firmly while rolling out the patch
With a good seal you can see the outline of the ribs in the tube. All edges should be sealed down tight.
Inspect the inside of the tire for nails, thorns, etc. that might have been the cause of the flat tire. Here you can see a lot of rust on the inside of the rim. I used a wire brush to clean the rust out before re-installing the tube.
The tire is old and thin. You can see holes in the tire itself in this photo. I'll pick up a new tire and tube next time we're in town.
Just reverse the removal process to re-install the tube and tire. Be very careful that you do not pinch or cut the tube while prying the bead back over the rim and watch that you don't pinch the tube between the tire's bead and the rim when you air it up.
Now just put the wheel assembly back on the wheel barrow.
When I put on the new tire I will use a wire wheel on my electric drill and clean all the rust from the inside of the rim then I'll paint the inside of the rim and let it dry thoroughly before installing the new tire and tube. If you install the tire and tube while the paint is still wet you'll have a very difficult time removing either after the paint dries!