There are two basic ways you can work on Sudoku puzzles — physically, with pen and paper, and electronically (on a computer).
Whichever your favorite, you will need a couple simple tools I just want to briefly cover.
Because this is a web site, you may think I prefer to work on Sudoku puzzles on a computer, but actually there is nothing better than sitting down with a cup of coffee and a good old-fashioned Sudoku puzzle, on paper. Although I'll admit I usually use a computer to create and print the puzzle — refer to the previous page for my reasons there!
First, let's talk about pen and paper. Or, more accurately, pen, pencil, and paper. Yes, you should always have a pen and a pencil when working on a puzzle.
Why? The pen is for final decisions. You only use it when you know what the answer is. You never use it for guessing. In fact, I do not recommend ever guessing when it comes to Sudoku. You do not need to.
Once you have logically determined what answer belongs in a cell, using any number of the techniques to follow, you fill it in with your pen. That's what it's for.
So then, why the pencil if guessing is not recommended? I'm glad you asked. The pencil is for a cell's candidates. For many easy puzzles, you will never need a pencil. But for the more advanced ones, you will need to fill in each cells' candidates with a pencil. You will slowly eliminate candidates later, so you will need to be able to erase them. Going forward, I will refer to this as "Pencil Marking", and it is covered in great detail in the "Basic Techniques" section.
So what tools will you need if you want to do Sudoku puzzles on a computer? Well, apart from the computer itself, you will need a computer program especially designed to help you work on Sudoku puzzles. The good ones will do all sorts of stuff including letting you do "virtual" pencil marks, or even print puzzles for doing with a real pen & pencil.
Some websites out there have Flash or Java based systems that allow you to work on puzzles directly on their site without the need for additional software. But beware — you probably won't be able to save your work and come back to it!
Again, I'm partial to a program designed to run on Windows called "Sudoklue", but I encourage you to do your own research.