From what I've learned in the last few months, for very young kids, they pay attention to the child's ability to focus on an object.
(they did have 'pictogram' eye charts--which also caused issues, because my child has never seen an 'old style' phone, and didn't know that one

)
With modern equipment, meant pushing buttons so the objects off in the corners (lights, stuffed toys, etc) moved--and seeing if she was 1-focusing there (seemed able to see the object and retain interest) and 2-able to FOLLOW the object--so if she was watching the blue stuffed dog, when it walked from left to right, did she follow it with her eyes. (I'd imagine that an assistant w/ a toy on a stick was probably in place before the electronic gizmos

(the techs held various prisms/lenses in front of her eyes while they did this)
Apparently, kids have incredibly elastic lenses, so they can make themselves focus, but they can't always force their eyes to follow what they've focused on.
They did also dilate her eyes--because that keeps them from being able to focus--and then the doctor put on a monstrosity of a helmet (on the doc's head, not the kids

, and played w/ looking at the shape of her eyes and looking into the backs of eyes, to tweak the prescription they had so far.
Think of all the equipment that the eye doctor puts in front of your eyes at an appointment--now attach that to the doc's helmet--that way the kid wasn't batting things away.
That part was actually decidedly low-tech--it had prisms and lenses and some lights...and that was it. So nothing new and fancy. (and the doc could use the kiddo's favorite toy bunny as part of the 'game'--which helped. And Bunny ALSO got an eye patch when they were trying to limit which eye saw what

)
This is the closest I can get to a picture of it:
http://www.honolulueyeclinic.com/images09/pediatric_eye_exam.jpg--I would swear our doctor's had more things attached than that.