Tap a tile, then tap a number and a color. Starting clues are marked: a bar under a given number, a corner notch on a given color. The ledger shows which pairs are already on the board, which is where rule 3 does its work.
No puzzle needs guessing. Easy and Medium solve with tile checks alone: what one tile can still be, given its row, column and the pairs already placed. Hard strips clues to the minimum and needs line checks too (the only open spot in a row or column for a number or color). Expert also needs pair checks (the only tile left that can hold a number + color pair).
Hint describes the next deduction and highlights the tiles it relies on. Tap Fill it in, or press Hint again, to place it.