Basic: Naked Singles
Check an empty cell against its row, column, and box. If only one number remains as a candidate, write it in. This technique alone solves most easy puzzles. It is the first thing you should look for every time you scan the grid.
Basic: Hidden Singles
A hidden single occurs when a number can only go in one place within a row, column, or box. The cell might have other candidates, but this particular number has nowhere else to go. Scan each box for numbers that are missing, then check where they can fit.
Intermediate: Naked Pairs
Two cells in the same group that both have exactly the same two candidates form a naked pair. Those two numbers must go in those two cells. You can remove both numbers from all other cells in that group. This opens up new singles elsewhere in the grid.
Intermediate: Pointing Pairs
When a candidate in a 3x3 box is restricted to a single row or column, it can be eliminated from the rest of that row or column outside the box. The number must appear in this box in this row, so it cannot also be in this row in another box.
Advanced: X-Wing
Find a candidate that appears in exactly two cells in each of two rows, and those cells share the same two columns. The candidate must be in one pair or the other, forming a rectangle. Remove it from all other cells in those two columns. This is one of the most powerful techniques available.
Advanced: Swordfish
An extension of X-wing that uses three rows and three columns. The candidate appears in two or three cells per row, all within the same three columns. It follows the same logic as X-wing but is harder to spot. Look for it when you are stuck on expert puzzles.
When to Use Each
Easy puzzles need only naked and hidden singles. Medium puzzles add naked pairs and pointing pairs. Hard puzzles require hidden pairs and box-line reduction. Expert puzzles bring in X-wing, swordfish, and sometimes coloring. Build your skills one level at a time.