How do you know when you have sanded a piece enough to apply paint?

Depending on what you're project is, you sand til it's completely smooth and free of any unevenness or blemishes.

no slivers, and completely smooth.

Most of the time you just need to lightly sand to remove any gloss and smooth out any rough areas. You do not need to get down to raw wood, metal,etc. Wipe the piece down after sanding, prime with a stain blocking primer, I use Zinsser 123, the paint and seal with at least three coats of a water based polyurethane.

Depending on what your doing. Can you give me more details?

It just has to be not shiny

Oh okay definitely sand it as smooth as possible. Get all the rough spots with a low grit sandpaper like 80 or 60 grit. Then sand as smooth as possible with like 150 grit or 200 grit. It should help alot

you want it as smooth as possible

I don't think my comment came through. you need to sand it good Try using like an 80 grit sandpaper to get the hard stuff then smokth really well with a higher grit until smooth.