From the Disney Web site:

Pilot Your Own Adventure
Whether you have a need for speed or crave a relaxing excursion, we’ve got a boat just right for you. Cast off with your crew—enjoying theme park views and natural surroundings as you cruise our scenic lakes, lagoons and inlets.

Choose from a variety of watercraft:

Sea Raycer by Sea Ray® – seats up to 2 Guests; $32 per half-hour
Climb aboard and have a blast on these mini-speedboats. Drivers must be at least 12 years of age and at least 5 feet tall. Younger Guests may ride as passengers. Maximum weight: 320 pounds. Parent or guardian signature required for all drivers 12 to 18 years of age.
Boston Whaler® Montauk – seats up to 6 Guests; $45 per half-hour
Chart a course for fun on one of these easy-to-pilot, versatile and roomy boats. Drivers must be at least 18 years of age. Maximum weight: 1,650 pounds. These boats are restricted to the waterway in which they were rented.
Sun Tracker® Pontoon boats – seats up to 10 Guests; $45 per half-hour
Smooth and spacious, the perfect choice for larger parties. Drivers must be at least 18 years of age. Maximum weight: 1,900 pounds.
Rental Details

Reservations are not required; rentals are available on a first-come, first-served basis
Guests must be 18 or over to rent a boat and present a valid Resort ID plus a valid driver's license, state-issued ID or Military ID
Onboard smoking is not permitted
Passengers must wear the complimentary life jackets provided
Marina Locations

Bay Lake Tower at Disney's Contemporary Resort
Disney's Beach Club Resort
Disney's Beach Club Villas
Disney's Contemporary Resort
The Cabins at Disney's Fort Wilderness Resort
The Campsites at Disney's Fort Wilderness Resort
Disney's Grand Floridian Resort & Spa
Disney's Polynesian Village Resort
Disney's Polynesian Villas & Bungalows
Disney's Wilderness Lodge
Disney's Yacht Club Resort
The Villas at Disney's Grand Floridian Resort & Spa
I don't know exact hours of operation but, typically, they are available during daylight hours at the locations noted. Any of the locations around the Magic Kingdom would be a good place to rent. In the past, we've rented the little boats (Sea Racyrs). The last couple of times, we rented a pontoon boat.