A few principles of mine

Okay, so now you've seen the basic marking method that I use.  If you haven't already developed something similar, you should start, remembering these principles.

1.  Bring Either/Or to the Fore.
Find a way to indicate pairs, and a way to indicate twoshares.  After much trial and error, I've found it confuses me less to mark pairs that fit into squares inside the grid and indicate pairs that cross from one square into another outside the grid, but you can use symbols to distinguish them or the geography of the space if you prefer.

2.  Being Methodical doesn't mean A always comes before B.
Find a way to keep track of what you've done and haven't done.  This isn't critical in the early stages of the puzzle when you can eyeball a bunch of answers, but later it can make the difference between spotting a vital clue and total frustration.

3.  Doublecheck your answers.
Take the time to glance across and down to confirm you're putting the answer in the right place.  The majority of the time you can't solve a puzzle is because you got careless.  (Well, the majority of the time I can't solve a puzzle anyway.)

4. Practice Makes Perfect
While you're developing your system, or learning someone else's, use it all the time, even on easy puzzles.  That way you'll internalize your marking system's strengths and its weaknesses too.  (Mine, for example, is really good for things that come in twos, but not quite as good for things that come in threes.)

5.  There is no One True Way
As we get into arrays, I'll show you some alternate ways to work.  Because if I did sudokus the same way every time I'd get bored.

6.  The Metaphor Matters
More on this later.  But essentially, the words or notation you use when describing sudoku shape the ways you apply the logic.

7.  Bifurcation is NOT Cheating
Cheating in sudoku would be limited to putting answers into the grid which you hadn't arrived at logically, either because someone is whispering them into your ear, or you've been copying from the answer grid.  Everything else is fair.  Even Ariadne's string, however clunky it might be.  Nobody's giving you a grade on this stuff, after all!