The idea is simply to train a baby to stay on the blanket when you put him/her there. With some training, babies can learn to recognize the end of the blanket as a firm boundary.
As with all obedience issues, consistency is key. You don't need to be harsh, but do make your requirements clear and be consistent.
Put the baby on the blanket with a toy or two, and tell her to stay there. Stay near. When baby heads off the blanket (and she will!), tell her no in a firm voice and put her back on the blanket.
When baby heads off the blanket again (and she will!), respond the same way that you would the 2nd time she touches whatever you just told her not to touch.
Get the idea? If you can teach your baby not to touch your purse, your glasses, your [fill in the blank], then you can teach your baby not to touch the floor. This isn't mean or oppressive - your baby will play happily within the boundaries that you establish, just as your baby can learn to be content without digging through your purse or folding your glasses in half when she finds them on the end table.
You do know that babies can be taught not to touch those things, right?
Once the baby understands what is expected, you don't need to stay right next to her. You can move freely about the room, or leave the room briefly.
You can lay out a blanket in a friend's home and expect baby to play happily w/o breaking your friend's knick-knacks.