What is the challenge?

The SUDOKU 9X9 grid is made up of 9 3X3 grids. Each of the 3X3 grids is to be filled with the numbers 1-9 according to the following rules.

No number can be repeated with the 3X3 grid
No number can be repeated in a single row
No number can be repeated within a single column

Not too hard, right?

Depending on the skill level of the puzzle selected, certain numbers will be already filled in. So, the challenge is to find the right numbers to fit into the remaining open slots.

Looking at the above puzzle, I approach solving it using this method:

Start left to right scanning each set of three columns to see any two already filled with the same number In this case, I see the number 2.
Based on the rules, I know that I must have a 2 in each column. Column 3 is missing a 2.
Based on the rules, I know that I must have only a single 2 in each 3X3 grid. This means my 2 is missing from the 3rd column and the third 3X3 grid.
Only one opening there, so I fill it in.

Now, I repeat this logic across each of the next two sets of three columns.
Next, I perform the same scrutiny of the rows, three at a time.
I only fill in numbers that MUST go into a certain cell, at this point. Based on the rules, I can make only one further definite assignment in this pass -- 7

Now, I have to start looking at the combinations within the 3X3 grids.

I start with the grid which has the most cells already filled. In this puzzle I see that the lower left grid has 6 out of 9 cells filled. The missing numbers are 3, 6, and 8. Now, I use this logic:

The middle cell of this grid MUST be filled with either a 3, 6, or 8
Already in the COLUMN containing this cell, I see a 6 and an 8
Therefore, the ONLY number to fill this cell is 3

Now, I examine the other two bottom grids to determine whether my additional 3, helped determine the value for another cell in either of the next two grids.

In this case, I can add another 3 in the second and third grids.