This page explains how to find and catch Azelf in Pokémon Brilliant Diamond and Shining Pearl.

When Can You Catch Azelf?

You can catch Azelf after you have caught or defeated Dialga or Palkia at the Mount Coronet Summit.

Where to Find Azelf

Azelf can be found in the cave in the middle of Lake Valor, which is accessible via Valor Lakefront, in the area between Veilstone City, Pastoria City, and Sunyshore City. 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.