Repotting is a bonsai duty which we all do but possibly not as well as we could. There is a tendancy in the west to rush a tree into its final pot or repot far too frequently and instead of finalising the image sooner, we inadvertantly hold the trees development back.
There is no special secret, just doing it as well as you can without compromise. The soil that you use depends on the individuals locality and availability but I would recommend that you always sift your soils thoroughly. The Bonsai sieve sets often do not have the right sized meshes so you will have to improvise. In my soil the largest quantity is Akadama. Many people in the UK do not like it as they say it breaks down especially in our winters. Although this is partly true, a lot can be done to prevent this when you repot.
An example of this was when I was in Japan the first time. A customer brought trees in to be repotted which myself and the other students did. A few days later the customer brought some more pots in that he wanted his trees in so we had to re-repot. Once I had taken the trees out of their pots I realised how much soil I had crushed. Had I not been made aware of this the tree would have sat in this red mud for years and not grown well. So the trick is work the soil in to the roots carefully, not working one area of the root ball more than the other. Work in an order, starting at one edge of the pot and finish where you began. Don’t do a bit here and a bit there, be organised.
The addition of grit itself does not help drainage much. If you need to improve the drainage then up the particle size with careful sifting or use a product like Kiryu, Hyuga, pumice etc instead of grit.
The following images show an example repotting of a shohin Mountain Maple (Acer Palmatum) at the Taisho-en nursery in Japan.