Context menus (also called context sensitive menus) were added as an alternative way of interacting with the game, instead of command phrases. The default method of accessing these menus is a single left-click on the creature or NPC, but it can be changed to use shift-left-click instead. In order to do this, click on your paperdoll's "Options" menu, find the "Interface" tab (top one of the right panel, with the mouse icon on it) and check "Hold Shift For Context Menu". Pets have the following menu options (you must be within 12 tiles of the pet, and be the owner in order to use it):

As you can see, all wild, tamable creatures have a "Tame" option. You must be within 8 tiles of the creature order to use it. You can also use the context menu to stable or claim pets with a stablemaster, the same 8 tile radius applies. Note: you can not claim pets by name with this method!