Start with scanning
Scanning means looking across complete rows, columns and boxes for digits that are already present. Because a 6×6 puzzle has only six possible digits, simple elimination produces useful information quickly.
Naked singles
A naked single is a cell with only one possible value. Suppose a cell’s row already contains 1, 2 and 5, its column contains 3 and its box contains 6. The only remaining digit is 4, so 4 must go there.
You do not need written pencil marks to use this technique on a small grid; often the candidate set is short enough to hold mentally.
Hidden singles
A hidden single occurs when a number has only one possible position within a row, column or box, even if that cell could appear to accept several numbers at first glance.
For example, if a 2×3 box is missing 2 and 6, but five of its cells cannot contain 6 because of their columns, the remaining cell must be 6.
Use box and line interaction
A 2×3 box can help constrain a row or column. If a missing digit in a box can only appear in one of two cells that lie on the same row, then that digit cannot appear elsewhere on that row outside the box. On a compact 6×6 grid, this interaction often reveals the next single quickly.
Rescan after every placement
Sudoku is a chain of consequences. A number that solves one cell changes three units at once: its row, column and box. After placing a forced number, immediately rescan those three areas before moving somewhere unrelated.
Avoid random guessing
If you feel forced to guess, first look for a unit with only two or three empty cells and check the missing digits again. The smaller 6×6 format is especially good for learning logical elimination because each confirmed placement reduces a relatively large share of the remaining possibilities.