I had the same problem..i'm 37 weeks pregnant and it's been a lot better the past month or so..but yeah ever since i got pregnant i was always feeling lightheaded, and feeling like i was going to faint at any given moment. I asked my doctor about it and she suggested taking an iron supplement..even if your iron isn't particularly low, it still seems to help. At least it did for me. Takes a few weeks to notice any improvement though.
Another thing could be you're not getting enough water. The first sign of dehydration isn't actually thirst, it's fatigue. If you drink a ton of water it should help a lot..
I'm just speaking on my experience, but perhaps it will help for you!

Drink LOTS of water and take it easy. Take your time getting up and laying down. Be sure you're taking your vitamins too, like amber said, you need your iron.