If you can get your hands on a kickboard you can practice the breating seperate from the arms so you don't sink. Hold the kickboard out in front of you (lying horizontal in the water) and do flutter kicks with your feet. Put your face in the water so you looking pretty much straight down. Blow air out your nose as you kick along with your face pointing down. When you need air, turn your head to the side. For the first breath turn to one side and for the second breath turn to the other side, and so on. When you get more comfortable with this, turning and breathing, see if you can give it a try without the board, but still with both hands in front. When you need air, first pull with one arm, under the water (doing the stroke, basically) and when it is bent back, turn your head to the side and breath under your arm pit. THe hand returns to his position in front of you and you wait til you need to breath in again (rememebr to keep blowing bubles out your nose) before you repeat with the other arm. This is a drill to get you used to the breathing and pulling rhythm. When you do the actual stroke, you do not pause in the front and wait to need air, you keep pulling. When you are proficient at it and swimming most distances, you do not need to breath every stroke. You breathe in odd numbered intervals anywhere from every third to every 9th stroke (9th is pushing it IMO, I find 5 very comformatable).
A quick comment about the pull, because if you have trouble breathing your pulling stroke might not be perfect either. Your arm should be fully extended in front of your when you begin the pull (this is very important for a good eficient stroke and not just splashing around futily) and the pull should be strong and steady back, feeling the power in it. It should be close to your body. When you put the hand in the water in front of you (as far out as you can remember) it should slide easily into the water (not making a splash) and should be at your body center (lef to right).
Hope some of that helps. You can hold onto the edge (instead of a kickboard) to practice breathing or kicking if you want (I do it to practice kicking sometimes). And if you really cannot get this freestyle down (I was terrible at learnign to swim, it took me forever, but now I am good at it and love it) you can do the rbeast stroke if you know it. The breaststroke is probably more dificult to perfect with the breathing and the timing, but that doesn't matter hardly at all if you are just swimming to get fit and don't care about perfect form. Doing breast stroke, try not to bob up and down too much, breath in as close to the surface as you can, and remember to pull in close to your body (not out wide) as you get way way mroe power out of it and a much better workout. I have done whoel swim workouts with just breast stroke and no freestyle at all (sometimes because of shoulder problems) and it is great. I always use goggles because I swim with contacts and the clourine bothers my eyes, but if you don't want to get your face wet, a breast stroke variation where you just don't put your face in, can be a good workout.