There are numerous websites describing balloon rockets. Here's the Science Bob site. You can do a quick Google search to find others.
We started with balloons, straws, tape, and fishing line. Fishing line is preferable to regular string, because it is smoother, and the balloon rocket will be less hampered by friction. Reportedly, long skinny balloons are best, but we only had the big roundish kind.
Thread the fishing line through the straw, and attach the line to two points.
The project started in the living room, with the fishing line stretched between two pieces of furniture.
Later, it was moved outdoors and used stakes in the ground, so that the rocket could travel farther.
Blow up the balloon. Don't tie it, but pinch it closed with your fingers. Tape it to the straw, with the opening of the balloon at the back of the balloon, pointed in the opposite direction of the balloon's expected path.
Then release it!
We did this over and over again.
Occasionally, the end of the balloon stayed closed, and the air didn't release.
For fun, we tried taping the balloon to the straw so that the balloon was perpendicular to the fishing line.
As you might predict, the balloon spun around the fishing line instead of traveling along it.