There are two basic strategies for solving a sudoku puzzle:
(a) direct elimination; and
(b) the "splat" lines (the # symbol)
Many so-called "advanced" puzzles actually have multiple correct solutions, which means at some point you will simply need to make an (educated) guess, then back track if it is wrong.
Direct elimination is where you pick a blank spot in the puzzle, then see which numbers already appear in conflict in either the same box, the same row, or the same column. This will be enough to solve the "easy" puzzles, which usually have at least one or two rows with only one blank tile.
I call the 'hashing' step (as in the picture #, not the table) where you work off the inverse rule of direct elimination. There can only be (say) one 7 in each row and column. So, pick a box which doesn't have a number 7 in it yet, then work out which squares can't have a 7 in them because that row or column already has one. You will often find only one of the blank tiles is actually suitable for that number in the box. If you imagine each 7 which is in the puzzle as a line crossing out the places where a 7 cannot be, the blank tile which is not crossed out in your box is where the 7 goes.
As a general tactic you should keep alternating between the two. When doing direct elimination only look at tiles which line up with the numbers in other boxes which are currently missing from this box. When doing hash elimination only bother with the numbers which are almost all done, and are only missing from one or two boxes in that area of the puzzle.
And if you are really stuck I can email you a java suduko solver which will print out all of the valid solutions for a puzzle.