Swap puzzles: follow the chain
Pick any misplaced tile and swap it directly to its home spot. The tile that was sitting there now needs a home too, so swap it to its spot next. Keep following this chain; each swap puts one tile home, and the last swap of a chain puts two home at once.
Played like this, a board of N tiles is always done within N − 1 swaps. Random swaps, or swaps that put no tile home, only add moves.
Read the picture before you swap
Spend the first moments looking at the preview. Find the tiles with clear features — eyes, fins, masts, the horizon — and place them first. Corners are easy to recognise because two of their sides are the picture's border. Plain tiles are best left for last, when there are few open spots.
Turn puzzles: decide, then tap
Every tile needs zero to three quarter-turns clockwise. Before tapping, decide how far it is from upright, then tap exactly that many times. If you overshoot, a right-click or Shift+Enter turns it back one step instead of three steps round the long way.
Work row by row so that every tile has finished neighbours to compare with. Continuing lines and colour bands across the joins are the most reliable check.
Hints without spoiling it
In both games the hint shows only one step: a pair worth swapping or a tile worth turning. Use it when you are stuck rather than at the start, and the puzzle stays yours.