The Evade stat of the pokemon using Minimize will increase by 1 step (termed BTLs in the Gameboy description) on the standard Accuracy scale.
A pokemon that is receiving the benefit from the use of Minimize will take double damage if the opposing pokemon successfully uses the move Stomp. The attack will still have to overcome the Evade modifiers created by the use of Minimize to do that damage, however.
Minimize will always fail if it has already been used 6 times by the same pokemon, without a move that lowers Evade being used on or against the pokemon using Minimize. This is due to the fact that a stat may only be raised by a maximum of 6 steps, until it is reset by the use of Haze or the pokemon is switched out normally. The maximum is the limit of how many increases can be applied to a stat. If another move increases the Evade stat of the pokemon using Minimize, the number of steps that it increases the Evade stat by will count toward the 6 step limit, and reduce the number of times that Minimize can be used appropriately.
An example of this last part might be if another pokemon who has both Minimize and Baton Pass used Baton Pass after using Minimize 3 times. If another pokemon that has Minimize is the receipient of the Baton Pass, it will only be able to use Minimize 3 more times before the move will fail.
