To defeat Leader Norman in Pokémon Emerald quickly, use Fighting-type Pokémon, as they are strong against his Normal-type Pokémon. A powerful choice is to level up a Machop or Makuhita, which can learn Fighting moves like Low Kick or Arm Thrust. Additionally, make sure to exploit his Slaking's truant ability by attacking during its turn of inactivity. Using status moves like Sleep or Paralysis can also help to disable his Pokémon temporarily.
maybe..defeat the fourth gym leader(Norman)..
After you defeat the Lavabridge gym leader, go to Norman (Your dad) and beat him. He will give you surf. Hope I helped! :)
After you beat leader Norman
You have to defeat the eight gym leader.
You beat Leader Norman, then someone gives you surf.
you go to the elite four and defeat them.
In Mossdeep City, Steven will give it to you.
After to defeat Flannery [Lavaridge GYM Leader] your rival Brendon/May will give it to you.
You get aerial ace when you defeat Winona the gym leader in Fortree city.
You battle Norman, the Petalburg City Gym Leader after you defeat Roxanne, Brawly, Wattson and Flannery in their Pokémon Gyms.
Any Pokemon with ice or electric moves
You Go left and use rock smash to open up the tunnel