At MIT, we covered the ground with a tarp, and covered the balloon with a bedsheet or clean fabric. It worked well for us. We were paranoid that without the bedsheet, we would prematurely let go of the balloon, especially when transitioning from inflating to launch. The larger the blanket the better - the balloon seemed to always fill up more than we expected
Here are some pictures of it in action, the courtesy of the Berkshire Eagle. Notice we created some makeshift tie-offs once the balloon got really big.