In order to capture Entei in Colluseum, you will have to battle the Cipher Admin Dakem at Mt. Battle, after area one.
His team consists of Metang, Golem, Swampert, Camerupt, and of course, the Shadow Entei at Level 40.
To easily capture the Shadow Entei, I would reccomend putting it to sleep, paralyzing it or otherwise giving it a status condition, and then throwing Great Balls (they seemed to work better than Ultra Balls throughout the game for me) like crazy.
If you want to, you could also Freeze it, if possible!
So, all in all, you can very easily catch Entei after defeating the boss (bring TONS of revives!).