I use everything above the stem that isn't green. Here's what we do, I'll try to explain this but I wish I had pictures.
Hold the flower in your left hand, kind if squeeze it shut with your finger tips and lay it down sideways on a cutting board.
If you look close at the flower/head/stem, there is a little bulge where the stem attaches, then there is a little waist or narrow spot before you get to the flower itself. You are going to want to cut just a little bit above the waist (towards your left hand).
This is where skill comes into play. If you cut too low, everything stays intact and you have to cut again. If you cut to high, the green crown shaped pice will come apart in seperate crown points. If you cut just right, the green grown can be remove in one piece like a cigar band and the petals will all fall away.
This will make sense if you are looking at a dandelion blossom. Practice, practice, practice.... you'll hit the sweet spot 95% of the time after you get going.
My wife is better at it than me, little fingers seem to make it easier.
Here's what a cleaned batch of petals look like:
Hope this makes sense.