I would like to echo some points people are making about this being a LONG process for beginners. I am coming into swimming with no experience except for the survival type swim classes you get when you are little kid. I felt before this that I could swim pretty well and hold my own as far as not drowning goes.
Man, what a shock it was to find out that I could only swim 25 yards before I had to pull up and breathe like I just ran a 400m sprint on the track (I'm a runner first).
It's been almost 3 months now, and I can now swim about 150 yards without stopping, and can swim about 1000 yards in a 40 minute session. Now that I've gotten some base fitness, I'm moving to doing intervals. A typical training session for me lately is like this:
200yd warmup (rest whenever you need to during this, go slow and easy)
4x50yd drills (catch-up, hesitate, reach, quick, etc.) feel free to rest whenever on these, even halfway across :-), it's about technique!
5x50yd intervals (shooting for 1:00 each with 30s recovery)
3x75yd intervals (shooting for 1:30 each with 45s recovery)
200yd cooldown
I'm planning on moving to some 3x100yd intervals, maybe even a bit longer too. But I'm going at it the way my girlfriend is taking up a "Couch to 5k" program. Start with Run-Walk-Run before you just Run. I know it's frustrating that progress takes so long, but you will get there.
Another thing, be careful getting advice from books and really experienced people who have never coached raw beginners. They often say things like "keep a high elbow" when you have no idea what the heck they are talking about. Watch videos on YouTube and work on one thing at a time. It will come.
Peace!