Edge-guarding 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 his enemy leads to many strategies and mindgames.
Edge-guarding strategies
Attacking from on-stage
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.
Edge-hogging
A common way to edge-guard is to edge-hog, or grab the ledge so that the opponent cannot. Usually, an edge-hogger rolls, gaining invincibility frames and defending himself 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 his recovery.
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.
Jumping off-stage
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 he can defend himself, such as using aerial attacks or directing himself away from the edge-guarder. If the edge-guarder is able to land a powerful aerial attack far off-stage, his enemy will almost certainly die. If the edge-guarder, however, is unsuccessful, he puts his own life in jeopardy, being so far off-stage.