This is a two-deck game, and perhaps the best known of them. Forty Thieves is interesting in the way the discard pile first grows, then (in a successful game, at least) shrinks again. The two keys to success are knowing how to transfer builds by clever use of empty tableaus, and knowing when not to make an obvious play because it might block a more important play later.
(A personal note: Forty Thieves is one of my all-time favorite solitaires. It takes a while to finish a game, and it takes some room to lay it out; but I strongly recommend it to anyone who has the time and space to devote to it.)
In general, try to play low-ranked cards at first, and let higher cards sit in the discard pile.
Remember that in a two-deck game, every card is doubled. Don’t play a card from the discard pile if you can play its twin from the tableau, because it’s important to create as many empty tableau piles as possible.
Late in the game, use empty piles to reduce the size of the discard pile.
As a shortcut Solitaire Till Dawn will let you move full or partial builds provided you have enough empty piles available to have accomplished the same move one card at a time.