Well the vet will give the bunny a health check before hand. They will then draw the vaccine into the syringe and inject it into her. Check with your vet before hand that they are going to administer 10% into the skin / ear of the rabbit as this helps boost the effectiveness of the vaccine. Some vets don't do this even though they should. If they don't know what you are talking about ask them to read the manufacturers instructions.
Once you get her home she will probably be back to her usual self within minutes. Sometimes they can be a little quieter than usual for a few days as their body copes with the vaccine but if there is anything serious like loss of apetite then you should contact your vet.