What would rehabilitation/ recovery look like for someone with a brain transplant (assuming all the right nerves were properly connected and the like)? Would a person have to relearn everything if the body functioned fine prior to the new brain?
There personality and memories would be completely intact (although new hormone levels could cause some minor change), they would have to relearn all their sense organs and muscles.
Each person is wired differently, the connections from my eyes to my brain will not perfectly match the one from your eyes to your brain. Your brain learns to control your body and its wiring plan, and interpret the signals for your cellular layout, these will not match from person to person. Then you have the differences in the organs themselves, ear canal shaped changes the sounds as they travel down it, even if the wiring matched up perfectly everything would still sound wrong for months. The screwed up the signals from the inner ear will probably make the person horribly nauseous or dizzy for while.
Likewise the signals from the eyes will not match. Even if you reattached the right nerves everything would be a blurry mess until your brain learned to interpret the different patterns of signals, since depth perception appears to have a critical period you might never get that back.
the distances between your joints is different as is layout of sensory cells in the muscles and skin as well as the number of muscle blocks per muscles this develops as you grow, in a whole new body some muscles will be weaker than expected others stronger. With voluntary muscle movement you will start out incredibly clumsy, possibly very weak as well, until your brain figures out the patterns of your muscle connections and movement sensors. You see something similar in limb transplants but it tends to be much easier since it is tends to be one isolated part. they person would likely be unable to speak for quite a while while they learned their new tongue, throat, and mouth. Speaking of which they will have a lot of problems eating for a while and will be biting their tongue and cheeks all the time.
This mismatch in wiring will exist with every sense, with one exception. Smell would be the one sense little changed, you would have to get used to your new body smelling differently but your olfactory bulb and receptors are attached directly the brains so it is likely they would bring those along for transplant, along with a small chunk of the adjoining skull.
Of course this brings up an interesting point, a head transplant instead of a brain transplant would solve most of the sensory problems, although muscles would still give the same trouble below the neck.
Just to add to what John said.
Apart from physical problems, there will be a range of acoompanying psychological problems. We have a body image that is based on our real bodies (but does not necessarily fully reflect it, that's why our photos look strange to us). A new body will require a construction of a new body image.
Just getting used to new looks takes time (think plastic surgery). But depending on the condition and appearance of this new body, this process may go not so well. Your body recipient might be unsatisfied with body parts (a big thing for men, and even bigger for women in developed countries), colouration (e.g. eyes, skin, hair), flexibility, etc.
Another problem is going through the body relearning period. It will be very frustrating for anyone. It will be even more so for someone mature or physically very fit. Your patient will be like a newborn baby at first but without the survival benefits of neonatal reflexes. While we can expect some initial confusion due to an overload of sensory information, the cognitive function will return in full prior to the acquisition of the control over the new body. This situation can be very traumatic. Some patients might end up with a PTSD.
There will be also a significant change in social life. It is not polite to say but our looks play an important role in our relationships with other people. Beautiful people, for example, get promoted faster and get paid better. They are also considered to be more moral (at least in the US population studies).
Age also affects social sphere. If a 100-year old brain is transferred into a 20-year old body they might find it difficult to connect with people. A resulting person looks too young to be accepted by elders, but they experienced too much to feel completely comfortable with young people.
This is not an exhaustive list of possible problems, but I hope this helps.
Most 'knowledge' is housed in the brain. I am assuming by brain transplant you are talking about one person's brain going into another person's head. I assume that the connection is made to the spinal cord, say at the top of the spine, which is part of the CNS.
If so, then in theory (we don't really know) the person would not need to 'relearn everything' but would have to come to terms with being inside a new body. If "I" got a brain transplant the new brain would bring its own personality. So when "I" woke up I'd be very confused. "I" would need to understand that I had a new body. In one sense the transplant was in fact a body transplant, and the original "I" had died.
Some SciFi scenarios have people clone their brains, and then transplant 'their own' brain into themselves. This is silly, but OK, you still have similar issues.
Also, host rejection (immune/compatibility) and meds regimen would be part of rehab.