I did not go through this, but from experience of this issue, I would get an ovulation kit so you know when you are ovulating. Now you should only ovulate every other month with only one ovarian. Use the ovulation kit so when you are ovulating you will hAve the best chance of getting pregnant.
Its not true that you ovulate every other month. I also have one ovary due to surgery. Google ovulation signs and get ovulation predictor tests that measure LH surge. Taking your basal body temperature with a special thermometer every morning is the only way to confirm ovulation other than tests the doctor can run. Your fertile years will be shorter with one ovary, you probably have 10 or so years left depending on how old you are. I'm dealing with infertility now because of my surgery 9 years ago. Don't believe when people reassure you, insist on ovarian reserve testing, I wish I had. Your gynecologist doesn't know everything. Good luck!