In Dragon Age Origins for Xbox 360 you have unlocked the specialization that you want but how do you set that specialization for one of your characters

On their level up screen, the specialisation screen is on the first page opposite the statistics. Keep in mind that a specialisation can only be granted to a character once he or she reaches level 7, and then a second at level 14. Also note that the joinable NPCs can't be given one until Lv14, as they all start out with a specialisation already (except for Sten, but he only gets one in total, at Lv14).