Ok need some input here guys as I am not a 'ritual' type person.

On Monday night, the new moon/New Year, I need to bury somehting, put it to it's final rest.

I even have a cemetary to put it in, granted it's full of animals that have passed, but they were very much cared for.

Any input?

If you are ritually challenged, Novia, you might consider keeping it simple.  (not that this is simple).  Perhaps, treat it as a small funeral (or a large one if that is what is necessary), putting it to rest as if it were a loved one.  Since I don't know the situation/thing, I can only suggest, maybe getting a wooden box to represent a coffin (open or closed casket?) and write out a few words about your attachment to the "thing".  Play some funereal music and light some candles.  Then, when you feel that you can "let go", put it in the ground and place the dirt over it.  If you are creative, maybe you can even make a small headstone (cross?) with an RIP or some small epigraph on it?  
Suggestions...such as they are.  I think I would do this if I had something that needed to be buried. (But only if it was something that I was having trouble letting go of).  I don't know.  What do you think?

Pretty much what I was thinkin. Now just hoping I don't need a pick axe lol, for the frozen ground.

Ok, temporary internment done.

Now I rember why it is I don't do these sorts of things.

I think this is going ot be a very long night. It's gonna take me until morning to ground out. Sheesh I haven't been this high in ages, and remember now why I don't.  

Hell I'm even nauseous!