Egg Lay (たまご産み Lay Egg) is Yoshi's neutral special move. He sticks his tongue out, pulling in and swallowing any enemy touched near by, causing around 7% damage and turning them into an egg for a few seconds. The amount of time that the enemy remains in the egg is determined by how much damage they have. While trapped in an egg, one is open to attacks, although they cannot be knocked back, and only sustain half the damage from attacks while in an egg (similar to being frozen). Tilting the control stick rapidly back and forth and mashing buttons will help the victim escape the egg more quickly.
It is important to note that Yoshi has a few launch resistance frames in this move from the second his tongue latches onto another character to the moment the egg is laid. This is useful for 4-player battles, as the attack itself only affects one opponent, so Yoshi would potentially be vulnerable - the resistance negates that vulnerability. Another important aspect of this move is that it acts as an aerial grab. The only other aerial grabs are Ganondorf's Flame Choke and Dark Dive, Bowser's Koopa Klaw, Diddy Kong's Monkey Flip, Captain Falcon's Falcon Dive, Mewtwo's Confusion, Kirby and King Dedede's Inhale, and Wario's Chomp.
Egg Lay can be used in an attempt to put the opponent off-stage, but unlike suicide techniques, such as Koopa Klaw and the Swallowcide, opponents can usually break out well before they make it below the stage, even at higher percents; the opponent also remains in full control of their horizontal movement while egged, so unless they are already far offstage they should not be falling past it.
The usefulness of Egg Lay is increased a fair bit in Melee's Adventure Mode, where enemies eaten in sidescrolling stages are instantly defeated. The move cannot swallow enemies at all in Brawl's Subspace Emissary, but it deals a solid blow (13%) with above-average knockback.
In Melee, this can be used to perform the shrink glitch.
 Manual Descriptions
"Paralyze enemies by swallowing them and laying them as eggs."
"Snag enemies with your tongue and brender them briefly immobile within eggs."
Since his first appearance in Super Mario World, Yoshi's trademark move has been gulping his enemies using his chameleon like tongue. However, since Super Mario World 2: Yoshi's Island, Yoshi has been able to turn his eaten enemies into eggs. Throwing these eggs at enemies would be Yoshi's primary attacking method.