Give the situation time. Read your pet books or get your vet's advice on the situation. Be sure to groom your pet on a regular basis, especially if your dog or cat has long hair. It will look forward to being brushed and combed. It is also a good way to pick out fleas, ticks, etc. and allows you time to inspect your pet for any health problems.
Regular grooming is especially important for longhair cats who are prone to hairballs.
With regard to bathing your pet - dogs will tolerate it, cats hate it. Many people bathe their dogs several times a year. But consult your vet. Get a rescue sticker for your home or apartment. You can obtain one from a pet store or in some cases, a fire station.