I used what I had on hand, so this is how I made mine. Feel free to substitute or modify to fit your own needs and supplies.
1) About a 12 - 14" section of bicycle inner tube.
Take it from an area not including the valve stem. I prefer a heavy duty mountain bike tube for 2.5 - 3" tires so it gives the largest inflated balloon with the least curvature, but I have successfully used road bike and small wheel size children's bike tubes.
2) 3 - 6 zip ties.
Get the good, heavy ones that won't break when you pull them tight. It doesn't hurt to have extras.
3) About 2 feet of 1/2" ID vinyl tubing.
I used the clear vinyl tubing from a hardware store.
4) A car tire valve stem.
I prefer the long ones, but you can use a shorter one.
5) Good quality electrical tape.
This is to cover the sharp, pointy ends of the wire ties after you trim them to length. I used what I had on hand. Instead, you may use silicone sealer, tool dip, masking tape, or whatever floats your boat.
6) A little talcum or baby powder.
To keep the inside of the inner tube from sticking to itself.
7) Silicone sealer.
Optional to seal the ends of the inner tube.
7) A good, sharp knife.
To carve the valve stem and cut holes in the tubing.
8) A pair of wire cutters or heavy duty scissors.
To cut the wire ties.
9) A pair of pliers.
To pull the wire ties tight.
10) A bicycle tire pump.
1) Zip-tie one end of the inner tube closed about 1" from the end. Pull this very tight! If you have some silicone sealer to squirt inside the bunched-up area, it will help keep the air in. If you want to be certain it's closed, use a second zip-tie. Clip the extra tail off the zip-tie(s) and cover it (them) with tape, tool dip, etc to prevent the sharp end from puncturing the inner tube later. Trim the inner tube to about 1/2" from the zip tie(s).
2) Turn the inner tube section inside out (putting the zip-tie inside). A broom handle, screwdriver (handle end!), or similar long, blunt object helps, as does a little powder on the inner tube. Don't use the pointed end of a screwdriver or you may poke a hole in the tube.
3) Cut or drill 3-4 small holes in the vinyl tubing in the 6" or so closest to the end. If the balloon gets folded or the tubing ends up at an odd angle, the end of the tubing could be blocked. These holes help let air flow in and out if this happens.
4) Put a little powder inside the inner tube and roll it around. This is to keep the tube from sticking to itself or the vinyl tubing. Clean any powder off the inside of the open end about 2" in. Any powder in this area will hamper the seal around the vinyl tubing.
5) If you have silicone sealer, coat the inside of the opening on the inner tube about 2" in. This is optional to help seal the inner tube to the vinyl tubing.
6) Slip the vinyl tubing inside the powdered inner tube all the way to the end. Zip-tie the open end of the inner tube to the vinyl tubing. It's better to use 2 or 3 zip-ties here so you have more sealing surface, but it can be done with 1. Be careful not to pull them so tight you collapse the vinyl tubing. Trim the free ends short, then cover them with the tape, tool dip, etc. to prevent sharp ends from poking you.
7) Carve the large bump off the end of the valve stem so it just fits inside the vinyl tubing. This should be a snug fit.
8) Insert the carved end of the valve stem into the open end of the tubing and zip-tie it in place. Trim the ends of the ties and cover them to prevent unwanted pokes.
9) If you will want to release the air quickly, remove the core from the valve stem.
10) Put just a pump or 2 of air in the balloon to check for leaks. Submerging the balloon in a sink full of water will help find any slow leaks. If you find any, release the air, tighten the zip tie or add silicone sealer as needed, and test again.
11) If you used silicone sealer, release the air and set it aside for at least 24 hours to cure.
12) Inflate and deflate the balloon carefully a couple times to check for any thin areas or tiny cuts in the rubber. If you find any, it's better to cut the inner tube off and make another one than to have it fail inside you.
Normal caveats apply... Inspect your toys before each use. If you see any damage or noticable wear, throw it away! It's easier and cheaper to replace the toy than explain why you needed that trip to the emergency room. Use at your own risk. That said, I've had the same one for over 6 years, ymmv. Enjoy!