Why should I get my hormone levels checked over the course of my menstrual cycle? I want to have children, but am having trouble getting pregnant. My friend believes this could be a fertility issue and is suggesting that I get my hormone levels checked.

You. You should check your hormone levels to see if you are ovulating. The single most helpful test is the Progesterone level on day 21-25 of your cycle. This will indicate if you have ovulated. Also we often check a day 3 fsh (follicle stimulating hormone), lh (luteinizing hormone), and Estradiol level. This will assess the "ovarian reserve" and see if there is any component of polycystic ovarian syndrome. Your fsh should be less than 10 and greater than your lh level. You can check to see if your are ovulating with over the counter ovulation test kits.
They can help inform. Your physician. But first start simple. Are you having regular monthly menses? How old are you? Could there be an issues related to sperm? Are there any other relevant medical issues. Hormone levels can be helpful but the best advice would be to speak to your gynecologist about what specific tests might be relevant for your particular situation.