Is it legal to pilot a homemade balloon? Sure. Anyone can construct and fly a homemade engineless aircraft that's less than 155 pounds without permission from the Federal Aviation Administration. You don't even need a pilot's license. The balloon that sailed across Colorado appeared to be extremely lightweight and would probably qualify....
Do you need permission to launch a balloon out of your backyard? Depends where you live. In rural areas that aren't close to any airports, you don't need permission to launch a balloon, as long as you stay below 18,000 feet. (Falcon Heene's balloon reached just 7,000 feet.) It gets more complicated the closer you get to cities and airports.