“over their heads.” That is, over the heads of the cherubim, as the context shows.
“sapphire stone.” This could also be lapis lazuli. The blue color was associated with God and his throne (Exod. 24:10; Ezek. 10:1).
“the form of a man.” This is God, Yahweh, appearing in the form of a man, as is clear from the context. [For more on Yahweh appearing in human form, see commentary on Ezekiel 8:2 and Gen. 18:1].
The book of Ezekiel gives us a lot of information about God and His chariot-throne, which He traveled on when He came to speak with Ezekiel. The chariot-throne travels lightning-fast through the air (Ezek. 1:14), powered by four four-winged cherubim (Ezek. 1:11), and when it lands it has wheels and can roll (Ezek. 1:16-17). It is quite compact, and thus can park between the south side of the Temple and the Temple enclosure wall (Ezek. 10:3). The cherubim are close enough together that their wings can touch (Ezek. 1:9). Above the cherubim and the wheels is a platform that glistens like crystal and is likely somewhat transparent, allowing God to see the cherubim, wheels, and ground below Him (Ezek. 1:22). Upon the platform is a sapphire-blue throne, and upon the throne God sits in the form of a human (Ezek. 1:26). The cherubim are living creatures, and go wherever and whenever God instructs them to (Ezek. 1:20), and when they move they make a great noise like the noise of an army (Ezek. 1:24).
Given the human shape of the cherubim and their four faces looking in four different directions (Ezek. 1:5-6, 10), it is likely that when God traveled on His cherubim-powered chariot-throne it is sometimes expressed simply as “God rode on a cherub” (2 Sam. 22:11; Ps. 18:10). It is unlikely that God would ride piggy-back style on a cherub. Also, that God rides on a cherubim-powered chariot-throne explains why cherubim are referred to as God’s “chariot” in 1 Chron. 28:18.