Instructions
Restart your game, and locate Uxie in its cavern at Lake Acuity.
Save your game before going in to battle against the monster. This will act as an insurance policy in case you knock it out.
Battle the Uxie, and attempt to wear its life away into the red. If you have any Pokemon that know a sleep attack, that can make capturing the Pokemon easier.
Throw a Pokeball when Uxie is nearly defeated. If all goes well, you'll capture it. You may need to throw multiple Pokeballs before you capture the monster. If you accidentally knock the legendary Uxie out, reload your saved game, then start the battle over again.
Repeat the battle as many times as necessary until you capture Uxie.