All five abilities are available in a single container button, simply labeled "Call Pet." With this button they can be put on the Action Bar together in a single slot. They can also be slotted separately or called by macros using their individual ability names.
If you use [Dismiss Pet] when in battle, casting Call Pet will bring the pet back with the same health as when it was dismissed. If the pet automatically despawns because of range, Call Pet will summon the pet with full health.
Each Call Pet ability's tooltip will automatically change when assigned a pet, matching the pet's icon and assuming the name "Call <pet's name>". This alternate name cannot be used in macros; only "Call Pet <number>" will work.
Patch 9.0.1 (2020-10-13): Levels changed. These abilities were previously learned at level 1, 13, 32, 57, and 80.
Patch 4.0.1 (2010-10-12): Call Pet has been split into five abilities—one for each active pet. It is available from the moment a hunter character is created, and the quest Taming the Beast is no longer available.