You need to tell us what it is about your images that you don't like. Is there unacceptable blur (focus or motion?) or is it composition? Exposure? White balance?
I have a D90 but from discussions with other, the D800 exposure is the same.
For white balance, you can use the ice. Just initiate the custom white balance process and frame the ice. That will give you correct color. The ice also makes it very easy to correct WB in post processing, but when reviewing your images it's nice to have correct color, and Nikon's custom WB process is soooo easy that...why not?
For exposure, you can use the ice as well, spot meter the ice and set exposure to +2. If you're really in tune with your exposure, you can set it +2.3 (You should actually be able to go to +2.7 without clipping highlights.) The method of locking in this exposure is another matter. Many will say to use manual mode and set your aperture, shutter, and ISO. I personally prefer auto modes and AE Lock. Just depends on how you like to control your camera.
With sports shooting, there are a lot of opinions out there on what works...and for good reason. The best settings depend on the sport and on what the photographer is trying to accomplish, as well as the photographer's style and equipment. You'll get a lot of opinions, sometimes contradictory. Try them all. The recommendations worked for someone...it might work for you too. Here are mine.
Set shutter to 1/500s to start. If you're shooting in manual then set widest aperture and ISO for proper exposure based on the above. As I said, I like AE Lock, as that allows me to change aperture without changing exposure. Either way...
If you tend to focus and track a subject, then set your Area AF to Dynamic and AF mode to AF-C. The Dynamic area AF will use the selected focus point for focus...but once focus is established, the focus points around the selected point will assist in maintaining focus, should your subject move away from the selected focus point. AF-C will continually update the focus position of the lens, keeping the subject sharp as the distance between you and subject changes.
If you're framing an area and just capturing the action in it (such as the goal,) then Dynamic isn't much help...but it doesn't hinder either. When capturing a scene, I actually like Auto area AF. But it only works well when the subjects are the areas of greatest contrast in the scene. For example, white uniforms against white ice...maybe not. But red/blue/black uniforms...that would work great.
For me, I find that the trick to getting sharp shots is to fire the shutter right after focusing. I keep focus on the shutter, and I'll "drum" the shutter to pre-focus, and then for the shot I give a full press...no stopping at the half-press. The camera will try to focus, and continue to do so until it gets a focus lock. The shutter will immediately fire, given me the shortest time between focus lock and shutter.
On my camera AF-S is Focus Priority only, which I prefer over the Release Priority of AF-C. The D800 can go either way via custom settings. Basically, if the subjects of the image have focus blur, then I don't want the image. Some may counter, saying that if you don't use AF-C with continuous drive that you may miss the critical moment. I say that if it's blurred...I DID miss the moment! The only comments you get from blurred shots is "awww that would have been a great shot!" So I use AF-S, Single Frame, focus on shutter, "drum" the shutter while tracking, then full press. That works for me...may or may not work for you.
How you hold the camera is important as well. I use my right eye to look through the viewfinder. I used to use my left eye, but forced myself to use the right and it's made a big difference in camera stability. When viewing, I'll turn my head slightly to the left and press the camera into my cheek. That adds a lot of stability. Press the shutter smoothly...don't hammer it down while trying to catch the exact moment. Press your elbows into your body, and you should never have any camera motion blur.