In battle
Normalize makes all moves used by the Pokémon with this Ability act as though they were Normal instead of their usual type.
If the move Flying Press is changed by Normalize, it becomes a Normal/Flying-type move, but it only counts as Normal when determining STAB.
If the move Freeze-Dry is changed by Normalize, its ability to hit Water-type Pokémon super effectively is retained.
Outside of battle
Normalize doesn't have any effect outside of battle.
Pokémon Mystery Dungeon
In Pokémon Mystery Dungeon: Explorers of Time, Darkness, and Sky, as well as previously mentioned effects, Normalize turns the standard attack into a Normal-type move. It also makes throwing items deal Normal-type damage. This does not apply to fixed damage items (Geo Pebble, Gravelerock, Unown Stones, or Rare Fossil).