The wand of fire is quite easy to identify; engrave with it and it will burn into the ground. (Engraving into ice complicates things.) It is one of those directional attack wands; in emergencies, you can use it against most monsters. The wand shoots beams of fire, dealing 6d6 damage to non-fire resistant targets. It does an additional 7 damage if the monster is cold resistant. The beam bounces when it hits walls or targets with reflection.
You want to obtain reflection or fire resistance to guard against monsters employing a wand of fire against you. Otherwise, be careful to leave enough room so that your own bolts of fire do not bounce from a wall back at you.
A wand of fire's most popular use is to burn Elbereth into the ground. A wand of fire's Elbereth will never degrade, and only the player can remove the engraving (by making it disappear with a wand of cancellation, make invisible, or cold). It will also become useful should you find yourself slimed.
Intelligent monsters have a chance to carry scrolls or potions -- they are almost always destroyed by the wand.
Wands comprise 4% of all randomly-generated items in the main dungeon, 6% in containers, 5% on the Rogue level, and 8% in Gehennom. There is a 4% chance that a randomly-generated wand will be a wand of fire.