Rabbits can be found in tall grass by leaving piles of carrots on the ground nearby. It seems to work best if you move far enough away so that you can just barely see the carrots, and check back every 15-20 minutes. If you are lucky you will find some of the carrots missing and a small white rabbit or two nearby. You need both a male and a female rabbit in order to breed more. It is usually much easier for new players to trade for a pair of breeding rabbits from an established player, rather than using this method to find their own.
A rabbit hutch requires the following resources to build:
These requirements are not difficult except for the clay dome. A clay dome requires 400 clay be shaped on Pottery Deck for an hour to make a wet clay dome, and then it must be fired in a Vault Kiln for an hour to make a clay dome. It may be much easier to locate a nearby public Pottery Deck and Vault Kiln to use rather than building your own since they are very expensive buildings.
Each pair of rabbits eats 5 carrots every hour in the rabbit hutch. Rabbits do not stud -- you must have breeding pairs of 1 male and 1 female. Rabbits breed very quickly! Every hour, when the rabbits eat carrots, they also get a breeding check for each breeding pair in the hutch, which has a chance of producing one new rabbit. Unless you have a huge stockpile of carrots, one or two breeding pairs is usually plenty. Thousands of carrots are usually needed to keep a rabbit hutch operating all the time.
Since rabbits cannot be separated like sheep to prevent them from breeding, some owners build 2 rabbit hutches and place a single male in one and a single female in the other. Then they cannot breed, but whenever you will be around to check the rabbit pen often the breeding pair can be combined in one pen. You should never leave rabbits unattended for more than a day or two or they will quickly breed, devour all of the carrots, and then starve to death. Additionally, rabbits can run away due to overcrowding. While there doesn't appear to be a lot of hard data on this, it is generally accepted that if there are more than 20 pairs of rabbits in a hutch, there is a chance that they will run away due to overcrowding.
Slaughtering a rabbit produces 1 rabbit meat which can be used in cooking. Every time you slaughter a rabbit there is a small chance that a rabbit pelt will also be produced. Rabbit pelts are currently only used in research at Universities, and in building Marble Obelisks (-- and also in upgrading an Acoustics Laboratory?). High Dexterity will greatly increase the chance of producing a rabbit pelt. Live rabbits can be used for rituals such as The Test of Festivals and fed to cobras in a cobra pit.
Rabbits cannot be placed in any type of container such as a tent or chest, but there are two buildings in which rabbits can be stored. A rabbit hutch is obvious, but live rabbits can also be stored in a cobra pit. Some players store their rabbits in a cobra pit, and then move the rabbits to the rabbit hutch whenever they are running low and need to breed more. The cobras will eat the rabbits eventually, so make sure you have more than enough rabbits to survive to breed more later.
(See also: Livestock)