To catch Deoxys, you need to its home in Birth island.The only way to get there is by having the Aurora ticket,which is about impossible to get since it's been about 8 years! After that hop on a boat ride from the port in Vemilion City. Plus you'll need to stock on a lot of Ultra balls because this can be a hard Pokemon to catch.Make sure your Pokemon are over level 40 if u have Firered or Lv. 30 if u have leafgreen.

When u hop off the boat on the island,the game's music stops. Then your find a triangle shaped puzzle,with a black triangle inside it,that u have to solve before battling Deoxys. Here's a walkthrough on the steps on how to solve the puzzle:

Start at the bottom of the triangle.

Take a step down and move all the way to the left.

Take 3 steps right and go all the way up.

Take 5 steps down and go all the way to the right.

Take 3 steps up and go all the way to the left.

Go all the way to the right.

Take 2 steps left and go all the way down.

Take 1 step down and move all the way to the left.

Go all the way to the right.

Take 3 steps left and face down.

Save the game 'cause it's time to battle!

Examine the triangle - Deoxys will jump out!

Well that's it!