Or buy eye decals from hunterdnrc. lol
Yeah I was shocked when I found out how many custom painters actually do it this way, and of course all the production companies. I bought some from hunterdnc but haven't used them yet (I kinda want to learn to paint eyes). I also had trouble choosing which size decal to use, for the sculpts I was painting I needed an in-between size which wasn't on the sheet. An iris that's too small looks strange to me.
All the tips above are great. I'm learning too, and I use 000 and smaller brushes for eyes (every company uses a different sizing scale though which is a PITA). I tried the toothpick method which was handy for control, but I still prefer a very fine paintbrush.
I also bought a desk magnifying glass with built in LED lights that looks something like this:
Best thing ever for painting fine detail with tiny brushes. It just swings out of the way and acts as a great lamp when you're not using the magnifier.
If you don't already have tiny brushes, the smallest brush I've seen is 100/0 which I have on order but hasn't arrived yet. It was by a company called Artetje I think? I do have some Royal & Langnickel 20/0 and 30/0 brushes which are also good for eyes. When I see some of the pros painting they are using quite large brushes on the eyes and doing a far better job, so I'm sure skill trumps brush size at the end of the day.
When I find some time I'm going to spend a day just painting eyes onto a sculpt over and over again. A hairdryer between coats, and at the end strip off with acetone and re-paint. Hopefully 30 or 40 goes at just painting the eyes on will get me to a decent point