Do not attempt all 5 expeditions: only embark on 3 or 4. This is the most important thing to keep in mind in Lost Cities!

Drawing from the deck is vital. Obviously, if a good card is available among the discards, or you need to delay the endgame, take a discarded card. But otherwise, always take from the deck, because either it's a card that may benefit you, a card you can discard to buy time, or (best of all!) the card your opponent is waiting for.

If you have just one card in a suit in your opening hand, especially if it is a handshake or low card, and have no immediate good move, discard it to buy time. If it becomes valuable later on, you may still be able to snag it; even if your opponent takes it, that leaves them with the not inconsiderable problem of filling out that suit (and you can proceed to hoard any cards in that suit that you acquire later).

It's often more constructive to hold on to a suit your opponent is trying to complete than to try completing it yourself!

Do not be afraid to lose a small amount of points in a suit if it allows you to stall and continue drawing from the deck. Effective stalling (while you wait for the cards you really need) is the heart of this game.