Cycling is a process of developing enough nitrifying bacteria in the filter to consume all ammonia and nitrite as it is produced. Nitrifying bacteria are two main types of bacteria, one that consumes ammonia and produces nitrite, another that consumes nitrite and produces nitrate. Until the filters build up enough of these bacteria to have undetectable levels of ammonia and nitrite the tank is not cycled. In order to track this you need liquid test kits to test ammonia and nitrite daily until both are back down to 0, at which point the only thing you need to usually monitor is nitrate (which needs to be kept under 20ppm with water changes).
I suggest you buy API's freshwater master test kit. It has tests for ammonia, nitrite, nitrate, and pH.
Get a tape measure and measure the tank's actual dimensions so we can help you verify its volume. The last thing you need to is be thinking it is one thing but it is actually another.