This is intended to be a general-purpose question to assist new programmers who have a problem with a program, but who do not know how to use a debugger to diagnose the cause of the problem.
This question covers three classes of more specific question:
A debugger is a program that can examine the state of your program while your program is running. The technical means it uses for doing this are not necessary for understanding the basics of using a debugger. You can use a debugger to halt the execution of your program when it reaches a particular place in your code, and then examine the values of the variables in the program. You can use a debugger to run your program very slowly, one line of code at a time (called single stepping), while you examine the values of its variables.
A debugger is a very powerful tool for helping diagnose problems with programs. And debuggers are available for all practical programming languages. Therefore, being able to use a debugger is considered a basic skill of any professional or enthusiast programmer. And using a debugger yourself is considered basic work you should do yourself before asking others for help. As this site is for professional and enthusiast programmers, and not a help desk or mentoring site, if you have a question about a problem with a specific program, but have not used a debugger, your question is very likely to be closed and downvoted. If you persist with questions like that, you will eventually be blocked from posting more.
By using a debugger you can discover whether a variable has the wrong value, and where in your program its value changed to the wrong value.
Using single stepping you can also discover whether the control flow is as you expect. For example, whether an if branch executed when you expect it ought to be.
The specifics of using a debugger depend on the debugger and, to a lesser degree, the programming language you are using.
You can attach a debugger to a process already running your program. You might do it if your program is stuck.
In practice it is often easier to run your program under the control of a debugger from the very start.
You indicate where your program should stop executing by indicating the source code file and line number of the line at which execution should stop, or by indicating the name of the method/function at which the program should stop (if you want to stop as soon as execution enters the method). The technical means that the debugger uses to cause your program to stop is called a breakpoint and this process is called setting a breakpoint.
Most modern debuggers are part of an IDE and provide you with a convenient GUI for examining the source code and variables of your program, with a point-and-click interface for setting breakpoints, running your program, and single stepping it.
Using a debugger can be very difficult unless your program executable or bytecode files include debugging symbol information and cross-references to your source code. You might have to compile (or recompile) your program slightly differently to ensure that information is present. If the compiler performs extensive optimizations, those cross-references can become confusing. You might therefore have to recompile your program with optimizations turned off.