I suppose everyone has their own way of grouting, but the end result is the same. Here is how I grout a mosaic.
The first step is to gather all the supplies you will need throughout the process as it becomes terribly messy and you don't want to traipse around looking for something later.
I always have 2 buckets (one for grout and one for water), a spatula or wooden spoon for stirring your grout, plenty of sponges, rags, 2 surgical gloves (it's what I use because you can throw them away), water spritzer, mask( again, I use the surgical ones because you can toss it out).
The next step is to get your grout mixed. This is where the mask comes in handy as the powder from the grout can go everywhere. I am using "charcoal" straight from the box so there isn't any custom mixing here. I use the sanded grout as I think it sets better and looks nicer when completed. You mix what you think you will use, but if there isn't enough it isn't a problem to just mix more. If it were a custom blend, then you will need to make plenty the first go around as the chances of mixing the exact blend a second time is nearly impossible. Ad just enough water to give it a consistency of smooth mud. It should not pour easily.
Here it is all grouted. Lovely, huh? I leave it like this for about 10 minutes or less then start to take most of it back off with a sponge and water.