I was really unsure about this at first too! I knew I wanted to do safety eyes, but wasn't sure the way to make them look really good, or even what size to buy. I do like jungrrl says, but I'm going to elaborate a bit because I do a few additional things...
First, I make dots on the face where I want the eyes, measuring to be equally distant from the seam, then I make the tiniest clip possible on the dots.
Next, I load "eyeliner" (identical cut pieces of ultrasuede) onto the shank of a safety eye, if I'm doing make-up. I cut the eyeliner pieces how I want them before the next step.
Then I push the shank of the safety eye through the tiny hole in the Poppet head, which widens it to fit perfectly.
After the eye is in, I use a tip I found on an amigurumi site. I add a piece of cushy fabric to the inside. I basically cut a small hole in the cushy fabric and add it to the shank on the inside of the Poppet's head. As I understand it, this is supposed to smooth the appearance of the safety eye shank. I don't know if it's necessary, but it is easy.
Finally, I add the shank (press it on hard!).
BUT, I'm not done, because after that I stuff the head very firmly, and then thread a needle. I try to use the needle catch up the cushy fabric on the inside of the head and anchor it to the neck hole. It takes a couple of strokes. I do this totally optional step to try to sink the eyes in a little because I want my Poppets to look more realistic.
Then, as for what safety eyes to buy, I got 12mm to use on my Poppets, but 15mm for my house elves (but, for the elves I followed the eyeball tutorial that jungrrl recommended above). I liked the 12mm size especially because I didn't have any stretch to my fabric.
Here is a link to my first Poppet, where I wasn't very successful with getting any depth to the eye, but it shows the eyeliner I made, which I would be happy to explain more.https://www.craftster.org/pictures/showphoto.php?photo=592039&ppuser=320939#axzz2ZYWynDHZ
Really I ought to just get ambitious and whip up a Poppet head then give it some eyes for tutorial fodder.