I love making greys to use alongside the bright pure shades on my palette. Grey can be really quite beautiful, and they help to balance a painting. It is always useful to have some mixed ready to use so I mix mine before I start painting. I choose the main tube colours that I'm using and mix my grey from them. My intention is to have piles of mixed greys in a selection of values so that I have the correct value to hand.
The most obvious way of mixing a grey is to mix black and white together. But there are better ways to create more vibrant and lovely greys. Mixing two complementary colours and a little white is effective, because complementary colours 'grey' each other down. You can quickly reduce the intensity of pure colours by adding a small amount of the opposite colour on the colour wheel. Or add a little of a mixed grey.
I like to mix greys from:
Viridian and Magenta/Alizarin Crimson + white
Ultramarine and Orange + white
Burnt Sienna and Prussian Blue + white
But there are lots of effective combinations, it is worth experimenting.