Chlorine and test strips or a kit. Always keep chlorine in the pool whether you are in it or not, and test it often. Your pool will use more chlorine when it is really hot and when it is raining.
If your pool starts looking cloudy, add more chlorine, that is the first step before the algae shows up.
Once you fill your pool or if your eyes bother you take a water sample to your local pool store and have them test the pH, alkalinity, etc. They will provide chemicals to help balance the water.
Run your filter 24/7 - that helps the water stay clean, rather than constantly playing catch up... and clean the filter according to the instructions. Assuming it has a cartidge filter, that is easy to clean, unless you had an algae conditon, just hose it down really well. If there is algae soak in a chlorine / water mixture and then hose it down.
Get a pole and a skimmer net to scoop out leaves and bugs and soft brush to get what fell to the bottom up where you can net it or the filter can pull it out. You might also want to get an underwater patch kit for emergency use.
Good luck!