The very first step when you are planning to bathe a rabbit is to stop and ask yourself "do I really need to bathe my rabbit?"
Rabbits are very clean animals and groom themselves very often. You should only bathe a rabbit if it is absolutely necessary.
Here are a few good reasons to bathe a rabbit:
If they were sick, which resulted in messy stools,
If they are dirty enough that a small spot cleaning with a warm, wet, soapy cloth won't do the trick.
So if your rabbit is dirty and needs a bath here is what to do:
First you need to set everything up and get prepared.
Make sure you have rabbit-safe shampoo. Never use any shampoo that does not state specifically that it is safe for rabbits. A good brand to use is Super Pet small pet shampoos.
Once you have your rabbit-safe shampoo you need to get the bath tub ready. (if your rabbit was very small, you could possibly do it in a sink, but a tub is generally easier.)
Place a non-slip rubber mat or a towel down on the bottom of the tub so the rabbit won't slip.
Make sure the water is warm, but not too hot. (rabbits easily become overheated, but make sure the water is still warm.) Do not use cold water because rabbits take a long time to dry so using cold water may make them to cold.
Make sure you have towels handy for drying off.
Now get your rabbit and place him (or her) into the tub. Let them get used to the tub for a minute and then introduce the water. Don't get the rabbit wet immediately. Let the rabbit hear the sound of the running water and see if he will approach it himself.
Once your rabbit is calm, fill the tub up an inch or two with warm water. (I find that having the rabbit in warm soapy water helps to clean his belly etc, without the rabbit becoming stressed because most rabbits do not like having their stomachs touched.)
Let the rabbit get used to being in the water.
Then you can get your rabbit wet. Be careful to avoid the face, eyes, and ears.
Once the rabbit is wet you can lather him up with shampoo. Make sure to go slow and try to keep the rabbit calm. Be careful to once again avoid the face, eyes, and ears.
Once the soap seems to have done its job, you can rinse your rabbit off. Make sure you get off all of the soap.
Now you need to dry your rabbit off. Towel dry him first. You can use a blow dryer to make sure he is completely dry. Just remember to use the lowest heat setting. If you are bathing your rabbit during winter when it is cold you need to use a blow dryer otherwise your rabbit will be cold. If your rabbit does live outdoors or goes outside for playtime (in a enclosed area of course), they must be completely dry first! A damp rabbit outside could cause your rabbit to become cold, but in can also cause something to happen known as fly strike. (basically flies swarm and attack the rabbit, which can lead to the rabbit's death)
Once your rabbit is fully dry, brush him to make sure that there are no tangles. You should also brush your rabbit before giving him a bath, especially if your rabbit is a long-haired breed.
If your rabbit isn't terribly dirty, you can clean him off with a spot cleaning. Just take a warm, soapy cloth and clean off any dirty spots, making sure to rinse the soap off of those spots afterward. The Super Pet brand also makes wipes for small animals to spot clean them. These are fine to use but you should still rinse off the spots with a wet cloth. Be sure to dry anywhere you got wet.