Unless you are using sleep masks when playing blindfold games, make sure that the cloths you are using are thick and dark and can be folded or rolled up. They also need to be long enough to tie up securely.
A good example would be a t-shirt as you can fold it up and tie using the arms pieces. A tea towel is another good option. Make sure the material over the eyes is not uncomfortable, and that most of the face is not covered.
The less the blind man knows about the game before they are blindfolded the better, and total darkness is best. Try to discourage peeping but not to the point where the blindfolded person becomes frightened. To disorientate the blind man, spin them around ensuring that are confused about which direction they are facing. Make sure that you take it in turns so that you get to be the blind man too.
If your child has never been blindfolded before, explain what a blindfold is before blindfolding yourself or another family member. Give them a simple object and explain to your child that because the family member is blindfolded they can not see and have to use their hands in order to correctly identify the object without removing the blindfold.
Then blindfold the child while they are safe on your knee, explaining that there is nothing to be scared of. If they do get scared, remove the blindfold and start simple by asking them to identify a simple object that they use every day like a soft toy.