Ovulation prediction kits (or OPKs) detect the LH surge in your urine which happens shortly before ovulation. So, yes, they do work. However, if you have an irregular cycle it may take a long time for you to get a positive OPK which could get expensive.
I would recommend that you start charting. There are lots of free sites for charting, but I like FertilityFriend.com. Your basal body temperature is the only free way to confirm at home that you did in fact ovulate, and cervical mucus is typically as accurate as an OPK for predicting ovulation.
Your fertile times are based on when you ovulate. Most women ovulate 14 days prior to starting their period. That said, with your having an irregular cycle you may ovulate sooner or later in your cycle. The best way to determine your fertile time is with charting.