Disclaimer: This only works with traditional toilets with the toilet tanks that you find in residential buildings and if nothing is broken in your toilet!
TLDR: Hold down the flush lever a little longer than usual.
If you're new to toilet terminology, there's a distinction between toilet tank, which is the part that houses the lever, water, and all these parts you see in diagram, and toilet bowl, which is the part you excrement goes in and out of.
Here's a diagram, courtesy of https://removeandreplace.com/2013/09/09/fix-toilet-constantly-running-diy-toilet-repair-step-step/, of what my toilet tank parts looks like :
So the problem: the past couple of days, I noticed one of the toilets in my home sounded like it was running a water leak constantly. After some Googling and watching toilet repair videos on Youtube, I was able to diagnose the issue - a faulty flapper (the red part in the diagram) - by lifting the toilet tank cover and pressing down on the flapper using a ruler, which made the water leak sound stop.
To understand what's happening, you need to understand how these toilets work. When you pull down on the flush handle on the outside, it activates a sequence of steps:
Flush handle on outside is pulled.
Flush level attached to the flush handle goes up, pulling the chain up.
The chain pulls the flapper opens just long enough to allow about 40% of water to exit from toilet tank into your toilet bowl. The water exiting the toilet tank also causes the flapper to close. The flow of water into the toilet bowl triggers a flush of the toilet.
The big black ball-float inside the toilet tank goes down (because it floats atop of the water, which went down because water just exited the tank into the bowl). This triggers the your inlet/fill valve to open and refill your toilet tank with water until the correct level is reached.
If you have water which has lots of minerals (AKA "hard water"), it can cause your toilet flapper to harden over time and not function properly. That was what happened to my toilet. The stiffened flapper couldn't form a complete seal and water ended leaking slowly into the toilet bowl.
So I went to my local Home Depot and bought a universal flapper that had the same dimensions as my old one. It went into my toilet and viola, no more leaking water sounds after a flush. One thing I did notice was the flush was a little bit weaker than before. The flapper just didn't stay open long enough for the flush I was used to.
The good news is the whole process is mechanical and can be controlled manually via the flush level. If you hold the flush level down a little bit longer, the flapper would be held open a little longer allowing more water to enter the toilet bowl - leading to a stronger flush!
It should be cautioned that you will end up using more water. Thus, you should only do this if you need a stronger flush. Also, you should not hold the flush lever down for too long because it really does drain water fast and might even cause a second flush!