Companions are the animals that rangers are entitled to befriend once they have reached certain levels in the guild. Companions tend to follow around the ranger and can perform several tasks, but they shouldn't be confused with Warrior Mage familiars, which are quite different. While familiars can speak for the Mage and can be their eyes, the Ranger has no such benefits from their companion; it's more of a friend willing to help out the Ranger, rather than a mindless drone. While still babies, companions require an awful lot of care and are easily lost, but with a little bit of patience, they'll soon grow to young and eventually full-grown and be a lot more self-sufficient.
Currently, companions are the best way to learn the Animal Lore skill and if you're intending to be a horse wrangler one day or deal with the upcoming companions, this is the way to go about it. Eventually there will be more systems which take this skill into mind, so I always suggest a ranger get a companion as soon as they can, even if they don't always have them out.

A quick note on companions and the RTS (trailmarkers): companions and the trails do not mix, particularly baby companions. If you're intending to run any of the trails, you should almost certainly send your companion away or you run a fairly substantial risk of losing your new friend.

The method for 'controlling' your companions is to use the signal verb. Currently the verb says:

    Usage:  SIGNAL COMPANION TO . . .
         FIND <player>
         DROP <object>          GET <object>
         UNHIDE                 HUNT
         STAY                   STOP
         HIDE
         (plus some others)

        Example: SIGNAL RACCOON TO FIND ANSON
  

Although all of those commands are listed, some of them do very little.
As it stands, you can expect the following:
FIND <player> -- Young and full-grown raccoons and wolves will find said player if they are not currently in an area where companions aren't allowed, for instance houses.
FIND <player> AND WAIT -- Probably more important than simply finding a player, this is the main way of using your companion to transfer goods as the companion will actually wait to get an item in return before going back to their ranger.
GET <object> -- Young and full-grown raccoons and wolves will pick up an item on the ground assuming they're able to lift the weight and it's not a weapon. Babies will pick it up but not hold it.
DROP <object> -- The companion will drop the item.
HUNT -- Young and full-grown wolves will go off to hunt, this is a way to avoid logging off to have your wolf go away.
HIDE -- All companions seem to fail miserably.
UNHIDE -- If your baby raccoon hides from becoming frightened, this will get it to come back out.
JUMP -- The companion will attempt to jump into your arms, or if already in your arms, will jump down.
STAY -- I've never seen this work.
STOP -- Signals a companion to stop following someone.

Character requirements:
Wisdom, Intelligence and Discipline must add up to 36.
Hiding must be 50.
Perception and Scouting must add up to 70.
You must be at least 13th Circle.

Instructions:
Make sure you have plenty of wild corn.

Go to Leth. From the center of town, go southeast 7 times, then go gate, sw

put corn on ground
hide

When you see a raccoon, approach raccoon. If you get round time, continue approaching until the raccoon trusts you, then signal raccoon to jump and immediately leave the area. (If you don't a hawk or eagle will come and eat your baby raccoon.)

Special thanks to Laurie for this information

Character requirements:
At least 35th circle
15 in charisma
No debts on the mainland
No current companion
35 in animal lore

Instructions:
There seem to be a couple of places to get a wolf that I know of and both of them are near cougars west of the brook in the Crossings area. The most common one seems to be the base of the trail to ogres. Once you are there. You simply need to kneel, hold a bottle of milk in your hand, which can be procured at the shack in Arthe Dale, and wait for the wolf pack to come by. Once the pack stops and smiles at you, you will need to stand and approach pack.
Assuming everything ends up alright, you will suddenly have a baby wolf.

All wolves require feeding roughly once an hour, whether they're by your side or not, so if you log out for days on end, they'll be hungry even if you fed them right before you left. Baby wolves require milk which can be purchased at a number of places, including Arthe Dale and the General Store in Aesry. In the case of Aesry, you'll actually purchase a picnic basket, which then requires you purchase a bottle of milk which is placed inside of the basket. In order to feed your wolf the milk from the basket, you'll need to get milk, which results in a cup that you use to feed the wolf. Young and full-grown wolves want to eat raw meat and the meat must be fresh or the wolf will become poisoned and die. In order to get meat, you must carve <critter> You can then check if the meat is good by doing a smell meat. When you smell it, you must get: Sniffing gingerly at the meat, you notice a pungent but flavorful smell. otherwise the meat is bad and you should get something new for your companion.
Here is a list of carvables that I have found:

• Musk hogs - Crossing, Langenfirth/Theren
• Snowbeasts - Leth Deriel, Shard, Aesry
• Small Peccaries - Langenfirth
• La'tami - Shard (Undergondola), Aesry
• Cougars - Shard, Langenfirth, Crossing
• Heggarangi Boar - Hara'Jaal
• Bears - Haven

Baby wolves, much like baby raccoons, are pretty much useless outside of role playing. When they whimper, it's time to feed them milk. When they pace it's time to pet them. This tends to go on for quite a while. Although we don't have any absolute numbers, it would seem that the base time for your first wolf is something on the order of 50 hours by your side until it goes from baby to young. This time is apparently influenced by the number of wolves you've had in the past or perhaps the number you've had run away, although most of this evidence seems to be anecdotal. Recently I've been told by someone that had never had a wolf before that it took 82 hours in order for it to grow from baby to young and this was tracked stringently. After this it would seem to be another 100 some odd hours for it to get to be full-grown.

Both young and full-grown wolves are able to carry items long distances for you. You can signal wolf to find <person> and wait to get them to go and find this person and stay with them indefinitely. The key to this is to have the wolf pick something up first, doing signal wolf to get <object> first, where object is something that is currently on the ground and then sending them to this person. This will allow the person to pet wolf to have the wolf drop the item in said person's hand and wait. In order to have the wolf return to you, you must have the person the wolf went to give wolf <item> where item is any thing sufficient for the wolf to carry. Wolves have a carrying limit that they cannot exceed and will ignore offers of items too heavy. In addition to overly heavy items, they will also ignore offers of weapons and will not pick them up off the ground. A common way of getting around this is to put said item in some sort of a container, such a sack of pouch. Wolves can only carry one item at a time.

Recently, wolves have become trackable. Although I don't know what the requirements are for this ability, I've heard people with as low as 116 ranks of scouting have been able to track them, though there appears to be a hard minimum of 50 ranks in animal lore. In this case, one of the most practical applications seems to be the ability to find deaders. You can track wolf then use the same signal command used earlier to find the deader and track to get to the wolf. There is a delay probably based on distance for your wolf to find the person, but once the timer is finished, you'll be there very quickly. This ability does have some distance limitations and you will not be able to follow them across bodies of water or things of that nature.

Young and full-grown wolves also have the benefit over raccoons of their same age in that you can signal them to go off to hunt which will allow you to be rid of them while you go find meat or go into a place where wolves aren't allowed. This can be quite handy, but when they return, they will be hungry just as though they hadn't eaten. Also, full-grown wolves will, at random, pull people out of hiding in the room. It would seem that they can pull out nearly anyone, but start with the person with the least hiding skill. There is no way to force the wolf to do it.