A few notes I made up for some students recently on the topic of oil paint on glass animation:
Equipment & Materials:
Glass
You can use a cheap frame to start of with while exploring the medium, but I would try and get one with glass rather than plastic, at least if you wanted to get extended use out of it. The plastic will scratch up pretty quickly from the repeated cleaning which may make it harder to slide the paint around. Also depending on the type of plastic, it can become permanently stained very quickly by the oil paint.
Lighting
A lightpanel or lights with adjustable positioning
Oil Paint
Can be cheap to begin with though you will find the artist quality ones much easier to work with for extended usage.
Clove Oil/Glycerine
These are useful not toxic mediums to prevent the oil paint from drying and extending the working time. I prever Clove Oil but it can be harder to source. Glycerine works best when using it with the transparent method.
Plastic card
Useful for scraping and shoving paint around - a palette knife will scratch the glass quite easily so this is a useful substitute. It can be cut and shaped for variation in markmaking.
Toothpicks
Wrapping a toothpick (or similar wooden or plastic elements) in a cloth or napkin you can control forms quickly cleaning up silhouettes and picking out details.
Health & Safety:
Be sure to provide adequate ventilation, even without using a medium the oil paint itself can be quite potent. Also be sure to work with gloves since many oil paints are toxic when absorbed through the skin.
Lighting:

For using the oils diluted with a transparency, akin to Caroline Leaf's The Street or Miyo Sato’s work on Mob Psycho 100, you can work backlit with a lightbox/panel. This has the added benefit of not eating through as much oil paint, though it would be a good idea to use a medium like Clove Oil to keep it fresh, though glycerine can work to a degree too. These are more lung friendly mediums than turpentine and the like. The downside of working transparent is that you cannot be as bold with your colours and as usual you really need to pay attention to your palette and values to make sure things read and don't get too muddy. Monochrome with an accent colour can work the best, in my opinion.

If you are working opaque, like we did on The Bird & the Whale, you will need a more complicated lighting set up to get the lighting even enough without lots of highlights on the wet oil paint. I would suggest an arrangement like the above.
Using the opaque approach you can have more range in your palette and richer colours, but you will really run through the material, so be sure to test and play using both methods to see what will work best for your project and resources. Also for B&W we used multiple layers of glass so the BG could be isolated and not need constant repainting after being obscured by FG movement, but this really isn't that necessary and depends on the look and feeling of the project.
One final note on working with oil paint, if you are finishing up for the day mid shot I would suggest spraying the surface lightly with the medium of your choice and covering the animation area with a box or other shelter to prevent dander or dust sticking to it. Depending on your process you may be best to clean the surface completely so you aren’t fighting against crusty dry oil paint to get to your glass the next day.
Depending on the style you can pick and mix things but those are general rules of thumb.
If you are interested I can do a part two on how we worked with animation pre-vis to try and make the painting process less arduous.
Let me know if you have any other questions!
E