Green swimming pool water is usually due to an explosion of green algae living on the surface and around the edges of the pool itself. If algae is able to survive in an otherwise pristine swimming pool it means a number of things are not right with the water or with the pool equipment itself. Beyond it being a rather disgusting pool to swim in, the algae can harbour bacteria that can sometimes make kids ill, and an accumulation of it can clog pool filters and pool plumbing. It's important to get rid of it as quickly as possible.
Your pH is too high
The pH of your water being too high keeps the sanitiser from working effectively and allows both green and brown algae to grow at a rapid rate. This could be your main problem or just one of your problems.
Your chlorine levels are too low
Chlorine is used in pools to keep algae and other bacteria from collecting and living in it. If these levels are too high they will burn people's eyes when they are swimming in the pool or cause reactions to their skin--chlorine is very poisonous in high doses. Yet if the chlorine levels are too low algae and bacteria will start to grow. This combined with another problem will give the bacteria in the pool the ability to proliferate.
There's something wrong with your pool filter
Pool filters are supposed to clean out impurities and small organisms and bacteria that can grow and spread from minuscule crevices and divots in the sides of the pool. If the pool filter is not working properly, these things will not be filtered out and bacteria will accumulate to the point that it won't be affected by chlorine or the pH levels.
Not shocking the pool enough
Shocking the pool on a regular basis kills early algae growth and keeps the water from being cloudy. This is a bit of a responsibility for a new pool owner but it is important to get into the habit of doing. If this isn't done at least once a month--and depending on the make-up of your pool water, twice a month--then green algae will start to build up.
Too Much Rain, Too Little Sunlight, Too Many People
Green algae can begin to grow after a lot of rain, which waters down the pH and chlorine content in the pool water. Also, sunlight is a great oxidiser and rain knocks out the sunlight--or if the pool doesn't get a lot of sunlight anyway, then you need to add oxidiser to the water, to keep the algae from getting started. A large number of people getting in the pool regularly can change the pH and chlorine content and up the bacteria content. This can also lead to algae proliferation if the levels aren't checked and adjusted after a party or shocked beforehand.