Debugging and fixing 'Undefined Variable' errors in Laravel involves several steps, ensuring that you understand the issue before attempting to correct it. Here is a step-by-step guide:

1. Identify the Error: Start by locating where exactly the error message is showing up on your website. This could be either during page load or when trying to access a variable from a controller, model, or view.

2. Check Variable Assignment and Scope: Confirm that the variable you're trying to use has been properly assigned in its respective scope (controller, model, or view). If it's an array, ensure you are accessing the key that exists within it.

3. Use dd() Function: Laravel provides a handy function called dd(). It allows you to dump and die out of your PHP code. This can be very useful in debugging as it stops script execution after dumping the variables.

    $variable = 'your value';
    dd($variable); // this will print $variable's value and then stop.
   

4. Check for Null or Undefined Variables: Ensure that your variable is not null or undefined before attempting to use it. This can be achieved with a simple isset() function in PHP.

       if(isset($variable)){
           // Use $variable
       }else{
           echo 'Variable is not set';
       }
   

5. Use Logging: Laravel has its own logging system. You can use the Log::info() method to log your errors. This is an excellent way to keep track of any unexpected behavior on your site.

       \Log::info('Variable not set');
   

6. Check Routes and Blade Files: Make sure that all routes and blade files are correctly referencing the variables you are trying to use. If you're referencing a variable in a view, make sure it exists in the data passed into that view from the controller.

7. Update Laravel: Keep your Laravel version up-to-date as new versions often include bug fixes and improvements that can address issues like 'undefined variable' errors.

8. Read Error Logs: Always refer to your server logs for error messages related to 'undefined variables'. These can give you valuable insights into what might be causing the problem.

Remember, when debugging these types of errors it is essential to keep track of where in the code they are occurring and why that section of code would throw an error with a certain set of inputs.