This page explains how to find and catch Uxie in Pokémon Brilliant Diamond and Shining Pearl.
When Can You Catch Uxie?
You can catch Uxie after you have caught or defeated Dialga or Palkia at the Mount Coronet Summit.
Where to Find Uxie
Uxie can be found in the cave in the middle of Lake Acuity, which is accessible southwest of Snowpoint City, in Route 217. Talk to it and you will battle it. It is level 50. If you defeat it, it will reappear here whenever you defeat the Elite Four and Champion for the first time, or you defeat them in rematches. It only stops reappearing after you catch it.