Fire Fox (ファイアフォックス Faiafokkusu) is Fox's up special move. When he uses it, Fox charges the move while being surrounded by flames (Melee and Brawl only), and then he flies in the direction inputted on the control stick or d-pad. The move has a fire effect throughout the entire move. Falco and Wolf have similar moves, Fire Bird and Fire Wolf, respectively, though, while the word "Fire" is in its name, Wolf's version has no fire.
Fire Fox is Fox's primary vertical recovery move. The attack can deal around 28% damage, provided the opponent is hit by both the charge-up and recovery. Fire Fox, out of all the Star Fox characters' recoveries, covers the greatest distance. However, unlike Wolf and Falco's versions, Fox's Fire Fox only hits opponents once, not having many multiple hits during charge-up or after being executed. It is highly likely to return to the ledge of the stage by using Fire Fox to recover, due to its long traveling distance. Additionally, if Fox hits the ground before the attack ends, Fox will slide on the ground in a wavedash like manner, cancelling any endlag from the attack.
In the original Super Smash Bros. for the Nintendo 64, Fire Fox was notably different from Super Smash Bros. Melee and Super Smash Bros. Brawl. Instead of being surrounded by fire, Fox charges the move without flames around him (and was pulled down by gravity at a reduced rate), and then propelled himself with an explosion, similar to PK Thunder 2. The charging does not inflict damage.
Interestingly, the author of the Prima strategy guide was apparently unaware that the attack can be aimed, even though the move has been aimable throughout the entire series; he suggests that its only use is attacking players from beneath.
 Description from the Melee Instruction Booklet
Charge up power, then blast off. Also use it to get back to the stage.
 Description from the Brawl Instruction Booklet
Charge up and fly in the direction you tilt the Control Stick, covering long distances.
Firedashing is a nearly useless Fox technique discovered by Hylian that involves using Firefox to bounce off of the stage and edgehog. The technique is present in both Super Smash Bros. Melee and Brawl.
To perform the technique, the player stands on the stage, facing the target ledge. They then jump and use Firefox diagonally into the stage, heading towards the ledge. Upon collision, Fox will bounce off the stage and, if spaced properly, fall right to the edge. If the player holds the control stick/d-pad back (towards the edge) as Fox falls past it, he will grab onto the edge, thus edgehogging.
However, given that the technique requires incredibly precise spacing, anyone who can aim Firefox that well could just as easily use it directly to the ledge, because Fox/Falco's up special moves will grab onto the edge from any direction as long as the control stick/d-pad is tilted towards the ledge when they encounter its sweetspot radius.
 Fire Bird
Fire Bird (ファイアバード Faiabādo, Firebird) is Falco's up special move in both Super Smash Bros. Melee and Super Smash Bros. Brawl.
Fire Bird is almost identical to Fire Fox, but with some small differences. Unlike Fire Fox, which only hits an opponent once after Fox starts moving, Fire Bird can hit opponents with multiple small hits after a few frames when the move is charged and when moving, followed by a stronger finishing blow similar to Lucas' PK Thunder 2. On the downside, Falco travels a shorter distance than Fox or Wolf. Its best use would be vertical or diagonal recovery because it has lots of start-up, short distance, and Falco falls almost straight down after using it, meaning it can easily be edge-hogged or hit out of. To maximize the usefulness of Fire Bird, one should try to position Falco exactly under the ledge and use it completely vertically, because then it can sweetspot more easily. Fire Bird burns opponents during the charge-up animation in Brawl, unlike in Melee.