Take a foam pad to put under your sleeping bag so you are not lying on the cold ground with just a thin compressed sleeping bag between you and the ground.
One of these, for example: http://www.rei.com/product/374059

Also put a plastic sheet under the tent floor (or above the floor, but I've always put it under the floor). Cut the plastic so it doesn't stick out any further than the edge of the tent floor so it doesn't catch rain and funnel it between the sheet and the floor. Use seam sealer on all the seams in the tent floor. Hopefully your tent has a rain fly. Good luck!