Where can I find and how can I change the thermostat and the gasket of a Toyota Corolla 1982?

I am not personally familiar with that particular car, however, they all are basically the same. Follow the upper radiator hose from the radiator to the engine. That is more than likely where the thermostat is located. Look for an aluminum housing held on by 2 or 3 bolts and is rounded enough for a thermostat to sit in. Changing the gasket is obvious. Just make sure to clean the old one off completely or it will cause the new one to leak. Gasket sealer is not really necessary but most people put some on anyway. If you must put sealer on the gasket, don't use much to prevent such a mess. You can use RTV sealer and just skim a thin coat on one or both sides of the gasket. That will help keep it in place while installing the housing.