Otterhounds should be groomed about once a week. Not only is this a great bonding time it is also a very important time to check for any health issues. The more your pup is used to being handled the better it will be should a vet need to do an examination. 
The coat should be groomed using a slicker brush, a wide tooth comb or a pin brush, checking for any unusual lumps or injuries as you go. After the coat is brushed the  eyes, ears and teeth should be checked to make sure they are clean and have no dubious smell to them. The feet and pads should be checked for injury or foreign objects, the nails trimmed and if needed the hair between the pads can also be trimmed. Some people like to keep the beard trimmed for hygiene reasons, I find a good towel rub after a drink does the job nicely.
As for bathing, I rinse  the legs down with a hose after walks to get rid of any debris, sometimes they get a total hose down if they are particularly grubby and maybe shampooed once or twice a year. The coat contains natural oils which do a fantastic job of keeping them clean without much assistance. 
Otterhounds have a double coat which should not be shaved off, it is there to do a job, to keep them cool in summer, warm in winter and to repel water. 

As regards exercise we recommend pups have restricted exercise for the first year to protect the muscles and bones as they grow. Stair climbing, jumping, or fast twisting & turning play should be discouraged for the first year. Time taken now to protect hips and elbows really can help them when they are older. As a rule of thumb we say five minutes exercise per day per month of life, so a five month pup could have a walk of about twenty five minutes a day.  From a year onwards most of the growth is done and your hound can safely do as much exercise as he likes.