Sometimes I grout as I go. It will be usually when I think that the materials I am going to use next on the mosaic will be ungroutable, like Smalti or marble.
I am using here a light grey grout. It's my favorite color because on one hand it's dark enough to remain as it is, and on the other hand it's light enough if I want to dye it.
I clean it thoroughly before it cures.
In this case I think the grout is too light on the hair and clothes so I am using a black ink to dye the grout. I do it with a good small brush because I want to be very accurate. I mix the ink with a little water and also dip my brush in water each time before dipping it in the ink.
The grout is still wet at this stage. I love dying it with ink because it is totally dissolved in the wet grout and once it is dry it is permanent. However you can still clean it away with a wet cloth if you don't like it if you do it quickly before it dries.
Make sure when you clean it not to clean it towards the parts which you don't want to dye. Make sure the cloth you are using doesn't touch the non-black areas. In this case I made sure not to touch the face.
This is how it looks now after the dying -