Your question is so darn wide and general that few people would have time to write a wide general reply.
A short answer would be;
"talk to a lawyer" as well as an accountant and maybe a few other professionals
Try again giving some more detailed and defined info.
May I suggest that your question tends to lead one to think you are not ready to be a business person, "Getting a business" isn't like getting a puppy or a mobile phone.
I would gather all legal documents that you can find on the business and take to a lawyer. Always consult a lawyer when taking over a new business. You might be in for a surprise if you find out that the business your taking over owes alot of outstanding debts. Just food for thought.
Ha...I've been burned by this one.
My Reply: BE SURE
Legally sever the new business from the old business.
It's easier than you may imagine. All on paper, close the old business, open the new business. Once we even bought all the clients from a badly managed business for $1, sent out under new management welcome letters to all clients etc.
The key is to sever liability but keep all the goodwill / clients, records etc.
You don't have to keep it a secret from clients but it is really none of their business.