The cheapest way to heat your pool is to use the free heat of the sun, but the initial out lay for the kit is quite high. Lets have a look at whats needed to heat a pool, and how it can be done on a budget.
Every solar heating system takes pool water, pumps it through a heat exchanger, and returns the water to the pool at a higher temperature. The method of pumping the water is usually the pools filtration circulating pump, which can often be quite large, in the 1 to 2 horse power range. This means that to heat your pool you would need to run your filter pump for up to 8 hours a day, which uses 6000 watts of electricity a day or 6 kwh.
The second part of the system is the heat exchanger, commonly these are glazed solar panels with a pipe looping back and forth across the panel to absorb as much of the suns heat as it can, typically the area of the solar panels needs to be greater than 50% of the pool area, and often up to the whole pool area in size to give a sufficient increase in temperature.
The forth part of the system is a controller that ensures that the system only runs when there is a difference in temperature between the heat in the heat exchanger and the water in the pool. If the system was to run while the pool was hotter than the panels the heat would be radiated away.
A solar heating system using the traditional solar panels could cost you between $ 2000 and $ 4000 depending on the manufacturer you choose,
ALTERNATIVES
If you have ever left your garden hose laying in the sun you will know how hot the water can get, so lets consider using black ventilation hose to heat the water, you will need an area that is as large as possible, possibly a roof where you can loop the pipe back and forth without kinking it. The area needs to be flat, (no humps and bumps) but can be inclined. The water would be pumped to the top of the incline and allowed to run back to the pool picking up heat on the way, the more pipe that you can add to the run the better, think in terms of 500 meters of three quarter inch inside diameter tube. If you are laying a patio around the pool, lay as much of the pipe in to the concrete just below the tile level as the concrete will get hot in the sun and transfer that heat to the tube. The cost of 500 meters of black irrigation pipe should not be more that about $ 100.
The pump is the next thing to consider, the 1hp filter pump will cost around $ 0.75 to $ 1.00 a day to run, so lets look at a 12 volt dc surface pump that will lift the pool water to the top of the incline, and if you connect it to a solar electric panel will work all the hours of sunlight for nothing. the other advantage of this method is that you can do without a controller as the pump will only work when the sun is out.
You would need to make sure the pump you choose will lift the water to the height that you need, but you should be able to find a solar pump for under $ 200, which apart from the time it takes to install will give you a cheap solar pool heating system for about $ 300 with zero running costs