Make sure you're positive you want to do this, as starting a business will take a LOT of your time and attention. You should start by checking with your local city government. See if they have any information on starting your own business.
You will probably want to start a corporation, as it will limit your liability (if someone slips and falls and sues the play center, the play center may close as a result, but you don't want them to get your personal house & car as well).
You may thus want to consult an attorney to get them to file the articles of incorporation and make you and your husband the sole stockholders in the corporation.
Talk to a business real-estate person to determine what properties are available for you to rent to start a playcenter, and also talk to your city government to see if they have zoning requirements for a playcenter, or any special requirements for running a playcenter (they may require you to have someone trained in CPR and 1st aid to be on staff at all times, etc.)
Then you will need to talk to an attorney about making sure you have appropriate liability protection for the playcenter. Then you should shop around and find out what insurance companies will charge for business liability for this type of business.
After doing all that, you'll need to purchase your equipment & toys, etc.
Then you'll need to consider marketing your playcenter so people will know about it.
You'll need to establish pricing that will cover all of your expenses (there's a lot so far: property lease, staffing, liability insurance, equipment purchase, etc.).
Since the above describes a LOT of work, you should write out a business plan describing how you plan to do each of the above activities, and what timeline you will do them.
If you don't have enough cash yourself to start the business, you'll need the business plan to go to the bank to get a loan (they won't give loans unless you have a detailed plan of how you plan to make money!)
Good luck!