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Understanding the fundamentals of Java programming is crucial for tackling any coding task in this language. Java, like many other programming languages, employs variables to store data, which might represent numerical values, characters, or even arrays of values. These variables can then be manipulated and used to perform computations or control the behavior of the program.

For example, in the context of our exercise, variables such as 'hours' and 'payRate' are used to represent the number of hours worked and the pay rate, respectively. These variables can be of various data types like integers for whole numbers, floating-point numbers for decimals, and so forth, tailored to their use case in the program.

Control structures are mechanisms in programming that dictate the direction the flow of execution will take. In Java, and many other programming languages, control structures include loops (like 'for' and 'while') and conditionals (like 'if-else' statements).

They are incredibly powerful tools that allow programmers to create flexible and decision-making code. A control structure responds to the given input and proceeds accordingly, allowing for tasks such as iterating over arrays, repeating actions, and making decisions. The clear command in this exercise to multiply the pay rate by 1.5 given a certain condition is a perfect demonstration of a conditional control structure at work.

An 'if statement', also known as a conditional statement, is a fundamental control structure used in Java to perform actions based on whether a specified condition is true or false. The basic syntax starts with the keyword 'if', followed by parentheses containing the condition to evaluate, and then a block of code enclosed in curly braces that executes if the condition is true.

In the given task, the 'if statement' would be used to check if the 'hours' worked are greater than 40. If this condition holds true, the resulting action is to multiply the 'payRate' by 1.5. It's important to remember to use rigorously correct syntax to avoid errors – missing braces or incorrect comparisons could lead to unexpected behaviors. Code readability also matters, making it easier to spot mistakes and understand the program's flow.