In FfH 0.95g, it's often difficult to capture animals before they disappear from the map and normal barbarian units begin spawning. The easiest way to do this is to guarantee that your civ has Animal Husbandry as one of your starter techs. The Centaur Commune, Elven Empire, and Sshrathi Tribes all begin the game with this tech. Keep in mind that several of these civilizations are creative, and this strategy can be quite useful when going for the cultural win. Furthermore, although I haven't tried it, the Sshrathi start with Animal Husbandry and Tracking. They might be able to reach hunting, and field hunters before the animals leave the map
The second thing you will need is scouts, at least 3 of them. Replace as needed, as they may die. The first thing you should begin building is a second scout. Fortify your starting warrior in your city. You don't want him stealing xp from your scouts, or killing the animals you want to capture. You will need the scouts to reach 5 xp in order to promote them with combat I and subdue animal. There are two ways to do this - either begin a training yard after producing your second scout, and researching warfare as your first tech (for conquest), or "wasting" the first animal you fight on training. Both are viable options (and you will need to do the latter with your first two scouts anyhow).
Remember that scouts are a 2 move recon unit. Take advantage of this. Make your first move across flatlands (plains, grassland, tundra, or desert), and end your turn in a defensive tile (forest, jungle, or hills). Don't move too far from your borders. Remember that you will need to send those animals home through potentially hostile territory.
Pretty soon you should spot your first animal. With any luck, it will be a lion or wolf. Wolves are a gimme. They move 2, but only have a strength of 1, so your scout can take them easily with his +100% bonus vs animals. Lions are strength 2, but You should be able to take them if they are on a flatland. You want to attack your first animal, since you get more xp for attacking than defending. This should net you between 5 and 7 xp, depending on what you are fighting. Promote combat I -> subdue animal.
Once you have the subdue animal promotion, you're golden. Now, you need to protect that scout. Always, always, always end your turn in a defensive tile. If you can end on a forested or jungle hill, so much the better. Wolves will come to you. You will probably have to chase lions. If you need to heal your scout, do so on a forested hill, preferably one surrounded by flatland.
Lions can appear anywhere. Panthers can appear in jungles. Bears appear in forests. I'm not positive about tigers and wolves., but this should help your hunting a bit if you're going for the "full collection".
A word about bears (and less so, tigers). Bears have a strength of 4 (tigers, 3). There is almost no way that a scout can take out a bear. Even ending your turn on a forested hill, a bear will beat you about 3 times in 4, unless your scout is heavily promoted. If you spot a bear, your best bet is to run the other way. There is one exception to this, however. Sometimes, a bear will attack an opponent's scout or warrior and be wounded. Contrary to popular belief, a wounded bear is less dangerous than a fully healed one.
Also, avoid desert and tundra tiles. Deserts spawn strength 4 hill giants, which will decimate your scouts, and tundra spawn strength 3 skeletons. Since you can't capture either of these, just avoid those terrain types.
So at this point, you should have around 10 captured lions, 3 captured wolves, and maybe a panther or tiger. Be very careful returning them to your civilization. You may wish to escort them home with your scout. If they run into another animal, captured animals are typically killed. If escorted, you now have two animals. Keep in mind that no matter how much xp an animal gets, it cannot be promoted.
As soon as you see your first barbarian combat unit (warrior or scout), rush home with your scouts and animals. Currently, no more animals will appear, when this happens (although this will be changed in FfH 1.0), and you're just inviting trouble
This strategy works rather well if you plan to go Fellowship of Leaves, as you will want to upgrade your well-experienced scouts to hunters as soon as soon as possible after real barbarians start appearing, and Elven Studies is just a few more techs down the tree.
One final thing. Captured animals can enter opponents cultural borders with impugnity. Normal animals will never enter cultural borders. This means that if there is an opponent civilization that borders yours, you can send your animals safely home through their civilization, without open borders, scouting all the way.
Of course, when FfH 1.0 is realeased, most of this will be pointless, since animals will stay even when regular barbarian units are arriving. But, for now, hope this helps. Have fun with your new zoo!
The second thing you will need is scouts, at least 3 of them. Replace as needed, as they may die. The first thing you should begin building is a second scout. Fortify your starting warrior in your city. You don't want him stealing xp from your scouts, or killing the animals you want to capture. You will need the scouts to reach 5 xp in order to promote them with combat I and subdue animal. There are two ways to do this - either begin a training yard after producing your second scout, and researching warfare as your first tech (for conquest), or "wasting" the first animal you fight on training. Both are viable options (and you will need to do the latter with your first two scouts anyhow).
Remember that scouts are a 2 move recon unit. Take advantage of this. Make your first move across flatlands (plains, grassland, tundra, or desert), and end your turn in a defensive tile (forest, jungle, or hills). Don't move too far from your borders. Remember that you will need to send those animals home through potentially hostile territory.
Pretty soon you should spot your first animal. With any luck, it will be a lion or wolf. Wolves are a gimme. They move 2, but only have a strength of 1, so your scout can take them easily with his +100% bonus vs animals. Lions are strength 2, but You should be able to take them if they are on a flatland. You want to attack your first animal, since you get more xp for attacking than defending. This should net you between 5 and 7 xp, depending on what you are fighting. Promote combat I -> subdue animal.
Once you have the subdue animal promotion, you're golden. Now, you need to protect that scout. Always, always, always end your turn in a defensive tile. If you can end on a forested or jungle hill, so much the better. Wolves will come to you. You will probably have to chase lions. If you need to heal your scout, do so on a forested hill, preferably one surrounded by flatland.
Lions can appear anywhere. Panthers can appear in jungles. Bears appear in forests. I'm not positive about tigers and wolves., but this should help your hunting a bit if you're going for the "full collection".
A word about bears (and less so, tigers). Bears have a strength of 4 (tigers, 3). There is almost no way that a scout can take out a bear. Even ending your turn on a forested hill, a bear will beat you about 3 times in 4, unless your scout is heavily promoted. If you spot a bear, your best bet is to run the other way. There is one exception to this, however. Sometimes, a bear will attack an opponent's scout or warrior and be wounded. Contrary to popular belief, a wounded bear is less dangerous than a fully healed one.
Also, avoid desert and tundra tiles. Deserts spawn strength 4 hill giants, which will decimate your scouts, and tundra spawn strength 3 skeletons. Since you can't capture either of these, just avoid those terrain types.
So at this point, you should have around 10 captured lions, 3 captured wolves, and maybe a panther or tiger. Be very careful returning them to your civilization. You may wish to escort them home with your scout. If they run into another animal, captured animals are typically killed. If escorted, you now have two animals. Keep in mind that no matter how much xp an animal gets, it cannot be promoted.
As soon as you see your first barbarian combat unit (warrior or scout), rush home with your scouts and animals. Currently, no more animals will appear, when this happens (although this will be changed in FfH 1.0), and you're just inviting trouble
This strategy works rather well if you plan to go Fellowship of Leaves, as you will want to upgrade your well-experienced scouts to hunters as soon as soon as possible after real barbarians start appearing, and Elven Studies is just a few more techs down the tree.
One final thing. Captured animals can enter opponents cultural borders with impugnity. Normal animals will never enter cultural borders. This means that if there is an opponent civilization that borders yours, you can send your animals safely home through their civilization, without open borders, scouting all the way.
Of course, when FfH 1.0 is realeased, most of this will be pointless, since animals will stay even when regular barbarian units are arriving. But, for now, hope this helps. Have fun with your new zoo!
Unless you have axeman, which will earn good XP from killing them. 
