I want to paint my home's varnished window sills. How do I know when I have sanded them enough?
If you want to do a good job, I'd sand until you begin to remove some of the stain from the wood (in effect, sanding the wood)
Then I'd prime the wood with Zinnser Bin wood primer than paint over that.
They have a fast drying version of this; I tried it once; don't use it. you need to move very very quickly. Use the normal drying one and it'll give you more time to work with it.
Wood "sweats" and the stain will eventually come through the paint. Removing the varnish and priming it with a wood primer (not a wall primer) will seal the wood and keep the new final paint from flaking / showing stain from the wood.
For some of the few window casing's I kept in this house and haven't removed, it's held up awesomely for 3 years now. I also had to use a heat gun to get 3 layers of paint off, but thats a different issue. I wouldn't use a heat gun if its varnished. Sand it.
I did this same process to any wood doors that weren't painted and all the wood trim we installed after gutting the rooms.