It is proper to bow down on one’s knees when reciting Aleinu during the repetition of Musaf. One should bow until one’s head touches the floor. Before beginning the repetition, the Chazan should position himself in such a way that he will be able to bow without having to uproot his feet from their place. To the best of my knowledge, it is not customary for women to bow to the floor.
If the shul’s floor is stone, tile, cement, or concrete, one should place a towel or the like on the floor before bowing to make a separation between himself and the floor. This is because the Torah forbids bowing down on a stone floor (except in the Bait HaMikdash) as this was a pagan practice.
These items should be placed so that they form a separation between one’s face and the floor. This is more important than having a separation between one’s knees and the floor, as the Rambam writes, “to separate between their faces and the stones.”
The Mishnah Berurah permits using one’s tallit to separate between oneself and the floor. This is because a tallit is worn loosely on one’s body. Other articles of clothing (such as a sweater one is wearing) would not constitute a separation for this purpose.
