Not sure about where to buy these (if you can do so by calling, or in person). I don't see them listed on the Disneyworld website. So not sure about start-end dates. I would start by calling DisneyWorld by telephone. These are in the category of Annual Passes.
Even though wdwmagic.com and
https://disneyworld.disney.go.com/tickets/ don't mention the Water Park plus DisneyQuest annual pass, two other places do. First is Cheshire Figment's Ticket Sticky, "Everything About WDW Tickets," Post #3,
Annual Passes and Water Park Tickets. This was written in 2013 and perhaps outdated.
http://www.disboards.com/threads/everything-about-wdw-tickets.1452684/
...The other APs are the Water Park Hopper, the Disney Quest Annual Pass, and the Water Park Hopper Plus Disney Quest Combined Annual Pass. These do not provide the benefits such as discounts and are very limited. The only discount for the Water Park Annual Pass is renewal rates...
A current website with up-to-date WDW ticket info is Mousesavers.com. They have posted new Feb 22, 2015
ticket prices, and have a listing for the combined Water Parks and DisneyQuest Annual Pass.
http://www.mousesavers.com/regular-walt-disney-world-ticket-prices/#ap
Water Parks (Blizzard Beach and Typhoon Lagoon)
One-Day Water Park Hopper Admission (usable any time): $61.77 Adult (10+), $53.25 Child (3-9)
One-Day Water Park Hopper Seasonal Admission (usable any time except May 23-Aug 30 in 2015): $56.45 Adult (10+), $47.93 Child (3-9)
First Time Annual Pass: $117.15 Adult (10+), $105.44 Child (3-9)
Renewal Annual Pass: $101.18 Adult (10+), $89.46 Child (3-9)
Water Park + DisneyQuest Annual Pass: $148.04 Adult (10+), $132.06 Child (3-9) (no renewal discount)
DisneyQuest
One-Day Admission:$47.93 Adult (10+), $41.54 Child (3-9)
Annual Pass: $95.85 Adult (10+), $76.68 Child (3-9) (No special renewal price)
Water Park + DisneyQuest Annual Pass: $148.04 Adult (10+), $132.06 Child (3-9) (no renewal discount)