For Animals - Handle Animal
Handle Animal is the skill for handling animals. That's true of animal companions, and animals you happen to buy or find in the wild. For tricks the animal knows, it's a DC 10 check. For others, it's a DC 25 check.
Druids & Ranger animal companions get the Link special ability, which gives +4 on handle checks and lets a handle be done as a free action. As Handle Animal is a class skill for both classes, it's fairly straightforward for both of them to get it up high enough that they can't fail the roll to use a trick.
So yes, you still have to use the Handle Animal skill to get your animal to do a command. But if it's a trick and it's your animal companion, doing so is a free action and with a few skill points in Handle Animal you should never be able to fail the roll. It's essentially automatic at that point, for tricks. For other non-trick commands (and people without animal companions), it's more involved.
More Intelligent Creatures (like Familiars)
The thing with normal animals is that they're not very intelligent. Familiars start with an intelligence of 6, which makes them intelligent enough to handle differently. Some of them can speak, and at 5th level you can communicate directly with them, so it's more like ordering a henchman around than trying to handle an animal.
Advice on how to play this
Ultimate Campaign has some advice on how to do this. The PFSRD has reprinted it on the Familiar page. Here's some excerpts, the whole thing is really long to copy.
Nonsentient Companions: a nonsentient companion (one with animal-level intelligence) is loyal to you in the way a well-trained
dog is—the creature is conditioned to obey your commands, but its
behavior is limited by its intelligence and it can't make altruistic
moral decisions—such as nobly sacrificing itself to save another.
Animal companions, cavalier mounts, and purchased creatures (such as
common horses and guard dogs) fall into this category. In general
they're GM-controlled companions. You can direct them using the Handle
Animal skill, but their specific behavior is up to the GM.
Sentient Companions: a sentient companion (a creature that can understand language and has an Intelligence score of at least 3) is
considered your ally and obeys your suggestions and orders to the best
of its ability. It won't necessarily blindly follow a suicidal order,
but it has your interests at heart and does what it can to keep you
alive. Paladin bonded mounts, familiars, and cohorts fall into this
category, and are usually player-controlled companions.