Last Possible Number
Last Possible Number flips the question around: instead of asking which cell a digit goes in, it asks which digit a cell can take. Pick an empty cell, cross off every digit that already appears in its row, column, and box. If only one digit survives that sweep, that's the answer for the cell.
Focus on one cell
Pick any empty cell. Look at the digits already in its row — those can't go here. Same for its column. Same for its box. Whatever digit from 1 to 9 isn't in any of those three groups is a candidate. If only one candidate is left, that's the last possible number for the cell. Some books call this "cross-hatching" because you're mentally crossing out digits across three intersecting houses.
The only candidate
Every cell belongs to one row, one column, and one box and has 20 distinct peers. For the selected cell, exclude digits already placed in those three sectors and preserve any candidates removed by earlier sound deductions. If one candidate remains, place it. Pencilmarks make the current candidate state easier to inspect but are not a logical requirement.
Practice makes it fast
The proof uses a cell-to-digit view. A cell must contain one digit, and every other digit has been excluded by its row, column, box, or an earlier sound deduction. With exactly one candidate left, that candidate is true. This is the ordinary Naked Single deduction viewed through direct elimination.