Edgeguarding is the attempt to prevent an off-stage recovering enemy from reaching the stage. Players can achieve this in many ways, and the struggle between an edge-guarder and their enemy leads to many strategies and mindgames. The anti-strategy is the Guard Break.
What is Edgeguarding?
Edgeguarding is a critical technique in which a player attempts to prevent the foe from getting back to the stage or grabbing the edge.
There are two main methods of edgeguarding. One is to run or jump off the stage and attack, the other is to stay on the stage and attack the opponent when they recover should they fail to sweetspot the ledge.
Any character can edgeguard, although some are better at it than others. A great example of edeguarding is Fox's down special in mid-air. The player jumps off the stage, hits the opponent with a shine as they recover, jumps quickly to cancel the lag and recovers onto the stage. This is known as ShineSpiking.
Certain characters are worse at avoiding being edgeguarded. These are usually characters with very predictable recoveries (Captain Falcon) or very poor recoveries (Falco or Dr. Mario)
Examples of Edgeguarding
Bowser: Fire Breath, SHFFL Back-air on the edge of the stage.
Samus Aran: Homing/Heatseeking Missile (Left+B, Right+B), at edge of stage.
Ganondorf/Captain Falcon: Down Air on the very edge of the stage.
Mario/Dr. Mario: Side+B (Cape) on the stage, to make the characters turn and fail to grab the edge, jump off the stage and Back-Air.
Edge-guarding strategies
On-stage guarding
The simplest way to edge-guard is to stand at the edge and throw attacks - often a powerful forward smash, down smash or down tilt that can hit even a sweet spotting enemy. While this method of edge-guarding requires the least set-up, it is often thwarted by sweet-spotting or ledge-teching.
Throwing projectiles
In a similar strategy to sitting on stage, a character with projectiles (especially projectiles affected by gravity, like Peach's turnips or Mario's fireballs) can stand by the edge and try to interrupt a faraway, recovering opponent. This strategy is very safe, in that players are very unlikely to be hit while edge-guarding in this fashion, and it can be combined with both edge-hogging and attacking from on-stage.
Off-stage guarding
A risky, but deadly, way of edge-guarding is to jump off-stage and interrupt the opponent in mid-air. The recovering enemy has few options by which they can defend themself, such as using aerial attacks or directing themself away from the edge-guarder. When using this style of edge-guarding, most characters put their own life in jeopardy, being so far off-stage. If, however, the edge-guarder is able to land a powerful aerial attack far off-stage, their enemy will almost certainly die. Even if unsuccessful, the edge-guarder can often edge-hog the recovering opponent anyways.
With most characters, it is best to avoid using the second jump before hitting the opponent. Many characters will not be able to make it back without it. Jigglypuff and Kirby are very useful characters to use for this strategy. Their multiple second jumps allow them to go far off stage and deliver a side kick.
Edge-hogging
A common way to edge-guard is to edge-hog, or grab the ledge so that the opponent cannot. There are several ways to reach the ledge when standing on-stage. The two most common ways are to face away from the ledge and either short hop or wavedash backwards. Many players, when wavedashing backwards, make the mistake of standing too close to the edge before wavedashing, thereby air dodging off-stage and falling to their death. Note also that with some characters, it is possible to fast-fall the wavedash off the stage and in effect grab the edge sooner.
Usually, an edge-hogger rolls the moment the recovering enemy uses their third jump, gaining invincibility frames and defending themself against damaging up B attacks. Edge-hogging is effective against sweet-spotting, but can be beaten by an enemy that comes fully on-stage in their recovery.
When an enemy lands fully on-stage they are often caught in the lag of their third jump. Edge hopping is often the method to keep them off the stage. This leads you back into the starting position of choosing which edge guarding technique to use, but your opponent has a little more damage making it a little easier to edge guard them.
Deterrence
A somewhat underutilized ability, deterrence is basically fake off-stage guarding. The player would make to jump towards the opponent trying to recover, but instead return to the stage without ever engaging the enemy. If done convincingly, the opponent will attempt to evade the non-existent attack and hopefully miss the ledge or dodge right into a different attack.
While this strategy works against newer players, it usually requires a twist against more advanced combatants. In this case, doubles play is usually necessary. The SLAPAHO team (founded by Aaron Kirschner) is known for having Marth prepare a spike on an oncoming enemy from an above platform, while having Roy charge a Flare Blade below. From here, one of four things happen: 1) Marth connects the spike and KO's the enemy; 2) Marth spikes the enemy into Roy's Flare Blade; 3) in attempting to evade Marth's spike, the enemy lands in the hitbox of Roy's Flare Blade; or 4) in attempting to evade both attacks, the enemy completely misses the edge.