The best and cheapest way to get to Wild Wadi is using a bus!
There are other options like using a metro or a cab or even going on foot !
From each side of Dubai, you should look for bus routes number 81. When you catch a number 81 bus it will arrive you right to the Wild Wadi water park, it’s only 150-190 meters far from bus station to entrance gate and you need to walk only 3 minutes.
You can comment your hotel or your departure point so I can give you the best bus routes from your location to Wild Wadi in your comment’s reply.