Hi, I also lost an ovary 9 years ago due to a cyst. I wasn't trying to conceive until recently, but I do know I had regular periods. You can chart basal body temperature using a special thermometer to confirm ovulation. You should ovulate every month, but I do think I have skipped a few and had early periods because of it (21-25 days).
My doc told me that the remaining ovary does the work of both. Ovaries usually alternate (one pops out an egg one month and the other pops out an egg the next month), at least according to my doctor after losing one ovary, the other pops out an egg every month. Don't know how true that is, but at worst, if the ovary sticks to an every-other-month schedule, that is not so bad either. My sister lost an ovary to torsion, and when she later tried to get pregnant she got pregnant the first month she tried. I wouldn't worry.