For felting you'll need wool roving, a needle felting tool (mine is called a needle felting pen), and your amigurumi! I generally also like to have a photo reference of the character to get the expression right.
To begin, take the base color of your eyes and start there. I take the wool and roll it into the general shape of the eye, then place is it on the plush and stab just a few times to be sure I like the placement. Once I'm satisfied, I stab it in! Don't worry about completely filling it in at this point. You'll be layering.
You'll want to get both eyes even during the base color. Otherwise, you'll have a lot of pain and suffering later trying to make your poor amigurumi not cross-eyed! Here I have my bulbasaur's eyes shaped the way I wanted them. Make note that when you stab in your wool, it will shrink a little bit as it's compacted. Take your time, make your eyes bigger as needed.
Here's where the layering begins. Bulbasaur has red eyes, with no black pupils, and white reflection in his eye. So we'll start with red, then move on to getting the reflection correct after. Just like with the base colors, do both eyes and make sure you like it before you move on! As you layer up, you'll notice that it is a little harder to push your needles in. Use some force, you won't do any damage (except maybe to your fingers! Keep those out of the way!). The barbs on the side of the needle is what makes the wool tangle and stay in place, so you need the needle to go in at least past the barbs.
Here you can see what I mean by rolling the wool into the right shape before you poke at it with your stabby tool. This would be the last step for bulbasaur's eyes, but most characters would have a pupil and then the reflection. Once this part is done, now would be the time to fill in any spots that are see-through, or fix any shapes the you are unhappy with in his eyes. I decided to make his eyes larger at this point.
I also needle felted his spots, nose, and his toenails - his little toes are my favorite part! When you're completely done, you'll need to reshape his head and legs a bit by smooshing them around. Unless you pull hard at it, the wool should stay in place if it's properly stabbed in.
What if I mess up!?
That is the question! And, I did mess up. The photos with the pattern show black outlining around his eyes, and I wanted to do the same. I felt like it gave him more expression. So, I tried it! Guess what?
BULBASAUR HAS EYELINER!
I hated it. It had to come off, but I had never taken off anything I had felted before. I took a chance, grabbed my seam ripper and a pair of tweezers, and carefully took off all the black with no problems. I had to clean up and restab the eyes a bit, but they looked better than before I had even put the black on.