Start with three rules.
A standard Sudoku has nine rows, nine columns, and nine 3 × 3 boxes. Fill the empty cells with the digits 1 to 9. Each digit must appear exactly once in every row, column, and box. The numbers already printed in the grid are fixed clues.
The digits act as labels. You do not add, subtract, or calculate with them. A valid move is supported by the positions of the other digits.
Read the empty spaces.
Choose a row that already contains several digits. Write down the digits it is missing. For each empty cell, check the column and the 3 × 3 box crossing that cell. Remove any digit already present in either place.
A small example: a row contains 1, 2, 3, 4, 5, 7, 8, and 9. Its last empty cell must contain 6. If the intersecting column already contains 6, there is a mistake elsewhere to investigate. Do not force the entry.
This is often called a single. You can find singles by scanning a nearly complete row, a nearly complete column, or a nearly complete box. After placing one, scan its three intersecting units again. One certain move can create another.
Use pencil marks with a purpose.
If a cell has more than one possible digit, a small note can help. A candidate is simply a digit that has not yet been ruled out by the cell's row, column, or box. It is a possibility, not a promise.
Keep notes current. When you place a 5, remove 5 from the notes in the same row, column, and box. An old note can hide a useful pattern. You can also work without a full grid of notes by writing candidates only in one box at a time.
Look for one home for a digit.
A cell might have several candidates, yet still be the only home for one digit in its unit. Suppose a box is missing 2, 6, and 8. The 2 can go in two cells, and the 8 can go in two cells, but only one of the three cells can hold 6. That cell must be 6, even if its original notes also included another digit.
This is a hidden single. It comes from asking a different question: instead of “what belongs in this cell?”, ask “where can this digit go in this unit?” Both views use the same three rules.
Give every move a reason.
Before entering a digit, explain why it belongs there. “It is the only candidate left in this cell” and “it is the only possible place for 7 in this box” are useful reasons. “It looks right” is a signal to check again.
A digit that does not immediately repeat can still be wrong. Local legality does not prove that an entry belongs in the final solution. If you get stuck, recheck a recent placement, refresh the candidate notes, or step away and return to a different row.
A change of pace: word search.
Start with a distinctive letter in a target word, especially an uncommon opening letter or a repeated pair. When you spot it, follow a straight line and compare every letter. Check horizontal, vertical, and diagonal directions, including backwards.
A matching first and last letter is not enough. Read the middle letters too. In our browser game, choose the first and last tile; the game checks the full path before marking a word as found.
Try it on a real grid.
Choose a browser puzzle, leave the clock out of it, and aim for one move you can explain. You can use a hint when you want to see a correct next entry, then return to scanning the affected row, column, and box.
Rules reference
Nikoli: Sudoku rules and examples. The explanations and examples on this page are original.