Crescent strategy
In brief
Send to the foundations everything that can go there, use the piles to uncover the cards you need, use the wrap from King to Ace, save the redeals for when nothing else moves, and empty a pile only if it helps. These are tips, not rules.
Play toward the foundations first
Each card placed on a foundation uncovers the next card in its pile. The won game on the Examples page starts this way: the 2♠ from pile 1 goes onto the Ace of spades, then the following moves build the foundations up or down whenever a card allows it.
Think about both directions
Each suit has two foundations: one that builds up from the Ace, one that builds down from the King. A card can often go on either one; the right choice depends on the cards still buried. Since a card can move from one foundation to the other of the same suit, a bad choice can sometimes be fixed: in the same game, after 51 actions, the 6♣ on the ascending foundation could move onto the 7♣ of the descending one.
ascending spades foundation: 2 of spades on top, 2 cards; ascending hearts foundation: 4 of hearts on top, 4 cards; ascending diamonds foundation: 2 of diamonds on top, 2 cards; ascending clubs foundation: 6 of clubs on top, 6 cards; descending spades foundation: 8 of spades on top, 6 cards; descending hearts foundation: 7 of hearts on top, 7 cards; descending diamonds foundation: jack of diamonds on top, 3 cards; descending clubs foundation: 7 of clubs on top, 7 cards. pile 1: 2 cards, 2 of hearts on top; pile 2: 3 cards, 8 of spades on top; pile 3: empty; pile 4: 1 card, 4 of diamonds on top; pile 5: 4 cards, 5 of diamonds on top; pile 6: 2 cards, queen of diamonds on top; pile 7: 8 cards, 9 of clubs on top; pile 8: 6 cards, 10 of hearts on top; pile 9: 4 cards, 3 of diamonds on top; pile 10: 4 cards, 6 of diamonds on top; pile 11: 6 cards, 6 of clubs on top; pile 12: 5 cards, 7 of clubs on top; pile 13: 5 cards, 9 of diamonds on top; pile 14: 6 cards, 6 of hearts on top; pile 15: 3 cards, 2 of clubs on top; pile 16: 8 cards, 7 of diamonds on top.
Don't forget the wrap from King to Ace
An Ace and a King of the same suit, each on top of a pile, can be placed on each other. The move is easy to miss and often opens up a pile: in the won game, it is used 2 times, the first at move 10 (the A♠ onto the K♠).
Save the redeals for when you are stuck
The redeal changes the top card of every pile in one go. It helps most when many piles still hold several cards, and only when no useful move is left. In the won game, the 3 redeals come after 16, 35 and 45 actions, with 20, 29 and 32 cards then on the foundations.
Don't empty a pile without a reason
An empty pile is never refilled: it is one less place to put cards. Emptying a pile is only useful if its last card goes to a foundation or unlocks a move. At the end of a game, on the other hand, the piles empty one after another: the last 5 actions of the won game all place a card on a foundation.
Use undo
The app undoes the last moves one by one. Trying a line and then going back is allowed; only a redeal erases the history, which is why it pays to look carefully at the board before pressing the button.