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The user enters a semi-invulnerable state for the turn the move is used. The next turn, the user exits that state and deals damage to the target. If the move is prevented from being used after the user has entered the semi-invulnerable state, then the entire move is canceled, but PP is still deducted. The user cannot make a move between turns. The user can still be hit by Surf and Whirlpool, which will hit for double the usual damage, while in the semi-invulnerable state, or if it was previously targeted by Mind Reader or Lock-On, or if the opponent has No Guard. If the user holds the item Power Herb, the move will not enter the semi-invulnerable state and simply deal damage to the target that turn. The user does not take sandstorm or hail damage while it is in the semi-invulnerable state. This move also has an in-game effect that lets the player dive underwater in dark patches of water.
Two-turn moves are almost unheard of in competitive battling because it is just so easy for your opponent to simply switch out to a Pokemon that either resists the move or is immune to it; in other words, you gave him a free turn. In this fast and more offensive metagame, that's exactly what you don't want to do. Dive has only an average Base Power, and does not have an outstanding effect that would make it usable, like Shadow Force. When choosing a Water-type move, there are far more reliable options.
Waterfall is a much better alternative, having the same Base Power, perfect accuracy, a 20% flinch chance, and not requiring two turns.
Aqua Tail is a more powerful option with 10% less accuracy, also not needing two turns to take effect.