Been there, done that. When I was a kid I was frog-marched to a freezing cold lido by parents who couldn't swim, so needless to say, I ended my childhood unable to swim either. It was the sight of others having fun and the desire to try canoeing that motivated me at the age of 25. Obviously the help and advice you need will likely depend on your own particular bogey men, but here's what I've learnt:
Re: water on your face, you can keep your head out of the water ok doing breast stroke, but I knackered my knees in no time doing that, it was the twist on the joint as you kick that did it. If you're forced to progress to front crawl like I was, you'll never make a good swimmer if you don't like your face in the water, because lifting your head makes your legs sink and drag in the water. Swimming like that is utterly exhausting!
You can get nose clips, but my tip is to close your airway in your throat. Think of clearing your throat: ahem, well now do the ah without the hem, so that your throat is shut. Like this, you can move your chest and upper body freely whilst keeping the air in your nostrils (and hence the water) completely still. You may find goggles help if the chlorine makes your eyes sore, but I didn't, in fact the clear view to the bottom of the pool made me feel like I was falling out of a plane, and I kept losing my balance. (I could probably have got used to them, but I only tried a couple of lengths with a borrowed pair.)
Some will tell you to breathe out slowly whilst your face is in the water, but I never do. Not only are you throwing away oxygen, but you're also losing buoyancy, and an explosive exhale as you come up for air helps to clear the drips off your face so you don't inhale them and splutter.
Re: the actual swimming part, I spent quite some time getting nowhere before I realised that my own bugbear was starting and stopping confidently, not the actual swimming. I couldn't take my feet off the bottom and get my body from vertical to horizontal in the water without losing control of my movements. Stopping was the same but more so, if I needed to stop in a hurry I just couldn't get my feet back on the bottom safely.
The answer was to swallow my pride and go in the baby pool to practice, where the water was shallow enough to reach the bottom with my fingertips. I repeatedly pushed off the side, glided, and then practiced rotating myself in the water in complete safety, so that I quickly got the hang of how to rotate myself in all 3 axes at will. In fact, having got back in the big pool, I discovered that the need to curl my legs up in the small pool was actually a big advantage in any water because your body will roll much easier and faster when it's in a ball than stretched out straight. If you want to change your attitude in the water easily, bring your legs up toward your chest, rotate, then straighten them again.
Once I could start and stop confidently, I went back in the big pool and just swam, it didn't seem to need any learning after that.
Floating: it's easy to say when you're not in a panic, but know that if you keep your lungs full of air, you will float even if you keep still. There's just enough buoyancy to keep your face above water with your head tilted back, but not if you try to lift your arms out of the water. You'll sink without the air in your lungs, so to breathe, exhale and inhale quickly, then hold it.
Treading water: despite the name, it's far less effort to use your arms. Vertical in the water, hold your arms horizontal on the surface, and sweep them forwards and backwards whilst tilting your hands like the pitch on propeller blades, it's so effortless you should be able to keep it up for hours. (For your survival certificates you have to tread water with your legs whilst waving your arms in the air, and that's exhausting!)
