I would like to know how I can find out if my eye surgeon is very experienced in cataract surgery.

Probably OK but ask! This is a standard procedure, quite simple for almost any ophthalmologist; probably no worries. (Asking if an ophthalmologist is experienced in cataract surgery is almost like asking if a carpenter is good at hammering nails into wood!) But if in doubt, just ask how many procedures s/he has done and how things turned out. Most surgeons are happy to share such data with their patients.