Toilet problems with valve

Typical toilets in my part of the world rely on a float connected to the valve that shuts off the water when the tank is full. Without pictures, I'm just assuming your toilet is similar to mine. These floats are usually adjustable, but in my experience it is not uncommon for the valve to fail and require replacement.

First, see if you can adjust your float. Open the toilet tank, and locate the float (it should be on a hinge or slide allowing it to move up and down with the water level). See if gently raising the float causes the water to shut off. If so, look for a way to adjust the float (usually by screwing/unscrewing a part of the mechanism). Posting pictures of the inside of your toilet tank would allow us to give more specific advice.

If manually raising the float does not shut off the water, you will likely need to replace the valve. These are typically sold with a new float as well, and installing a new toilet valve is a relatively simple DIY project. Before starting, make there is an external valve that can shut off water to the toilet!

Some fill valve have a washer in the top that can be removed and replaced. If so, you can avoid having to drain the tank to replace the entire assembly. On some models the top half slides up and down on a stem for adjustment. If you get the same model, you can also just switch the top halves and again avoid draining the tank.