You cannot mark your territory in Amethyst Mountain or Lost River. Typically, real wolves will not mark their territory unless they want to start or already belong to a pack. To mark your territory in Slough Creek, you have to first find and choose a den site. Once the den site is chosen, you mark your territory by pressing the 'P' key on your keyboard (for raised-leg urination), or by pressing 'H' to howl.
In multiplayer, marking territory is only available in the ‘Raise Pups’ game mode.