First, there are 2 types of iron the body needs, nonheme and heme. You can get one from red meat and one from plants like spinach. You'll want to consume with vitamin C containing foods, like red bell peppers, to increase absorption of iron. You may want to also avoid ingesting too much calcium at the same time as some studies have shown that calcium blocks iron absorption (but this was a controversial topic last I looked into it so do your own research).

When I was pregnant and planning a homebirth, I had this same problem and was being threatened with needing to switch to a ob/hospital if I didn't get it under control. So I ate lots of grassfed steak sauteed with spinach and red bell peppers cooked in cast iron for a little extra boost of iron, and I did great. I also decided to avoid dairy. Works fast.

PS iron supplements suck. There's no guarantee you'll absorb them, and they can start to cause bathroom problems. I always use food first to correct an imbalance as it's the form we are meant to take in, the vitamins in food are bioavailable, and its less likely to cause side effects.