I have a fairly large rural lot so I bury my pooches and invite family and neighbours over to say some words over the grave. We generally have a "wake" which is very helpful for yours truly! It gives me a chance to bring out my guitar and sing every dog song I know
One thing to keep in mind is to dig down over a metre in depth and well away from ground water sources or well heads. This is quite a job for me in that I live on top of the Niagara Escarpment and the soil is full of limestone and granite.