Most methods of repairing toilets are easy do-it-yourself steps. The real challenge of fixing a toilet is usually finding the part causing the problem.
A household toilet should have its own shut-off valve located somewhere near the fixture. Usually, its a chrome-plated compression fitting with an oval knob. So find that before making any repairs.
A tank's water level should fill to about 1/4" to 1/2" below the overflow pipe. Bend the float arm gently to adjust the water level; down to lower the level or up to raise it.
If the arm is hard to bend or needs to be bent a lot, unscrew it first to avoid damaging the ball cock assembly. Also, some assemblies have an adjusting screw on the ball cock valve to regulate the water level.
Check that the flapper (or tank ball) seats properly. Flush the toilet a few times and adjust the flapper until it seats. Adjust its chain connecting to the handle rod if needed.
If the flapper seats correctly, but doesn't stop water, clean any rust or buildup around the seat opening. If the flapper continues to leak, replace it.
A faulty ball cock valve (the assembly attached to the float arm) may fill the tank and cause water to run continuously down the overflow tube. Always shut off the water supply before removing the valve.
Sometimes, the ball cock seals can be replaced and the leak will stop. But finding and fixing the problem may not be worthwhile.
It's often better to buy the whole assembly so you're sure the leak will be fixed. Or upgrade to an in-line float which seems to operate and adjust a little easier than the arm-type float.
WARNING: It's easy to crack porcelain when tightening lock nuts so be extra careful when using a wrench. A condition called "back-flow" or "cross-connection" can suck tank water back into the water supply line; contaminating supply water if the ball cock valve is submersed.