Disclaimer; These pages contain advice only, you are advised to seek assistance from the manufacturers on the correct use of their tools.
Fortunately you don't need many tool and they are relatively inexpensive. The most expensive would be either a hammer and hardie, for hand cutting, or if you need to produce large amounts of stone tesserae then a wet saw. Below is a basic list of the things you need to start;
1. Cutter - whatever you need for the material you use for tesserae, this can be, tile nippers, hammer and hardie, electric wet saw.
2. Tweezers - For removing tesserae so you can keep your hands clean of adhesive/glue. Unless you are using 1mm tesserae I always use my fingers to place tesserae, even 5mm you can use your fingers, and mine aren't that small! Using tweezers to place tesserae is too time consuming. So, fingers in, tweezers out.
3. Gouge - If you need to remove tesserae that are set. Anything will do, so long as it has a flat or pointed end that can be placed between tesserae to lever them up.
That's it, you can add floats, trowels etc for cementing, things for cutting baseboards etc but as you can see it's not a huge list to get started.