What are some fundamental rules that you should have when you own a house with a pool and have young children?
In Australia it is the law that all pools have child safety gates around them. If that's not the case where you are from, I'd strongly suggest investing in one anyway, and being strict about keeping the gate closed.
Between 1996 to 2005, there were 245 children and young people who died as a result of drowning (3.5% of all deaths). 73 of the 245 drowned in private swimming pools or spas.
Teach your children very sternly that they are never to go anywhere near the pool without you, no running, etc., and of course teaching your children how to swim and all about water safety.
And the number of stories I have heard from parents who have just looked away for a moment, and then looked back and their child is in the water is so alarming. If you are supervising your kids, be sure that is exactly what you are doing (not reading a book, or anything else distracting).
Last of all, if you haven't taken a first aid course and learnt CPR, do it. The worst thing imaginable for me would to lose a child when I could have saved them if I had just spent that time to learn CPR.
One thing we tried which works well (assuming your children are old enough to have started to learn to write) was to have the children help write up the Swimming Pool Rules on a big piece of card or board. Then they help to fix these rules up somewhere near the pool.
The rules are the common sense things like "no swimming unsupervised", "no fighting" etc.
But the written notice helps them to understand that it's very very important, and having them responsible for creating the notice helps them to commit to it and take it seriously.
First, you need age-appropriate rules, so your children will understand and remember them. For example, "You are not allowed to go swimming without mommy or daddy" for a 3 year old, or "No horsing around near the pool" for a 6 year old.
Second, sign them up for swimming lessons, unless you're planning to hold them in your arms for the next several years whenever you're in the pool. In the long term, this is how you prevent drowning. Classes for children will emphasize water safety.
Third, CPR is very effective when performed by nurses and paramedics who do it for a living. It is rather less effective when performed by people who took a 2-hour class a few years ago.