By "singing" with certain frequencies, the elves are able to shape the crystal into practically anything. They use this to create a variety of equipment, as well as structures; their capital city, Prifddinas, was shaped in this way. The process of singing is still somewhat mysterious, and no human is ever known to have done so on a high level comparable to that of elves' singing.
Based on bits and pieces of information gathered in various quests, the process of crystal singing apparently involves emitting sounds of frequencies beyond the human auditory range; the crystal responds to those sounds by morphing into various useful shapes.
Crystal Singing can also be performed using bowls that have been shaped in such a way that their curves create a sound similar to the "Singing" normally performed by elves. Before the release of Prifddinas, and therefore before the player completes Plague's End, singing bowls have limited uses. They can be used to sing Crystal chimes and Crystal saws in Brimstail's cave. In the Ithell district in Prifddinas, you can sing Crystal tools, weapons and armour from the singing bowl there.
In the quest Within the Light, your character seems to begin learning the basics of crystal singing, as you enchant two crystals to teleport to the temple of light. The Prisoner of Glouphrie also indicates that other races than elves, such as humans and gnomes, also possess to an unknown degree the gifts necessary for crystal singing. However, it is unclear as to how much a human or gnome could further their gifts.