How do I level up an animal?

As far as I am aware there are two ways of increasing the effectiveness of animals in combat. This is of course assuming you mean increasing the existing animals, as opposed to simply replacing the m with better animals.

1. Gain Levels: This is by far the most common. Most classes, indeed I believe all, that grant an animal of some kind, be it via Familiar or Animal Companion, offer a progression that as you increase in level, the animal companion increases in power.

2. Apply a Template: Many templates are inherited but there are some that are acquired. Perhaps the most helpful immediately for you would be the Guerreiro template.

There are certainly many ways to gain better animals, but most that I am aware of are replacing the creature rather than improving an existing one.

Animals gain experience like every other creature type.

Monster Manual 1 has the following to say about levels and racial hit dice:

Monsters do not gain ability score increases for levels they already reached with their racial Hit Dice, since these adjustments are included in their basic ability scores.

In other words, racial hit dice = levels.

Therefore, racial hit dice are gained with experience points, the same as levels.

The Monster Manual gives three ways for creatures to advance:

1. Class levels (requires INT of 3, minimum; animals whose INT permanently increase to 3 or more convert to magical beast. )
2. Increased Hit Dice (see note)
3. Modelos

Increased Hit Dice: Intelligent creatures that are not humanoid in shape, and nonintelligent monsters, can advance by increasing their Hit Dice. Creatures with increased Hit Dice are usually superior specimens of their race, bigger and more powerful than their run-of-the-mill fellows.

Creatures of the animal type are still considered monsters by the rules, despite it sounding odd.

Most groups probably won't be thrilled with splitting the XP with the party animals. But hey, if your horses manage to evade the dragon and not get eaten, they've earned their XP.

My group has two treasured horses, Tasty and Crunchy, so dubbed after The Incident. They survived a wyvern attack, and have the scars to prove it; which they love showing off to the mares.

Note: the exact details of adding xp to monsters (including creatures of the animal type) is pretty much left up to the DM.

Familiars and animal companions have separate rules governing their advancement, see the respective class features.