Matching tiles on long horizontal line edges should be your priority as leaving those long lines will cause problems very soon.If you see four identical and free tiles - you're in luck! Match those combinations immediately.
If you see three identical tiles which are free to match - either choose a pair which opens up most new tiles or look for a quick ways to free the fourth one and match all 4.There are pairs which don't open anything new - it would be a good idea to hold them in reserve and match with another tiles. Always try to match pairs which lead to opening up most new tiles.Note the special Mahjong tiles (Seasons and Flowers) locations - these ones can be a great help. You will certainly find some good opening moves. Before making your first move in Mahjong Solitaire, take a moment to familiarize yourself with the board layout.