Drag slowly in a direction to preview what will happen with the tiles. If they are going to merge, the tiles will appear to overlap. If they will simply move, the tiles will slide over. Use this preview to decide if that move is your best. Drag back to your starting location after the preview to avoid actually executing that move.

Place a high-value tile in a corner and surround it with more high-value tiles. This will narrow the directions you have to move everything.

Keep high-value tiles together to make easy matches.