Pigment liner by steadler (0.05)
Sharpie/permanent marker with 2 tips
Pencil (I use faber-castell cuz it's hot)
Paintbrushes (size 0 or 2; I like the cheap nylon type, but a damaged hoghair does the job as well. Do not use bristle or something really stiff!)
Fine acrylic paints. I use pebeo, stevenson, and liquitex. Once you use the 'fine art' quality, you can never go back...

Sketch the eyes with a pencil and start by outlining the top with a pigment liner.
Lightly outline the rest; this step isn't necessary. I only do it because pencil marks aren't very visible.
It's now time to lay out your palette! See the general tips for advice on colours. (btw: I'm too lazy to fetch my palette paper...so I just use whatever cardboard is closest to me. In this case, from a kleenex box.)
Paint white around the iris (not the entire eyeball; it gets done last). This step is important because colours work in relation to one another. Therefore, the colour of the iris will look different against a skintone background instead of a white one.
Paint the base colour of the iris. This is generally the "eye colour" of the character.
Paint the bottom highlight
Paint the top shadow
Ok. It doesn't look like there's any difference, but there is: I've painted the pupil. It's supposed to blend well with the top shadow, but that depends on the reference picture.
Add in the top highlight bubble. Stick to your reference; there might not be a bubble in their eyes.
Once again, it doesn't look like there's a difference. But if you observe closely, I've darkened the outline of the iris.
The iris is finished. Now proceed to the outline of the eye. Paint black in the large areas; the thin areas can be done with a marker or pigment liner.
Now that the outline is more or less defined, you can paint the white of the eyeball.
Paint the shadows in the whites. Remember that an eyeball is, well, a ball! It's round, so the outer corners are generally shaded. In terms of colours, I like to mix black, white, and the base colour (it provides harmony).
Refine the iris and make sure it's got a clean edge agaisnt the white.
Outline the eye with a marker and/or a pigment liner.
Add the eyebrows, eyelids, mouth, and you're done! Congratulations, your plushie now has a face. ^_^