Truffles can be obtained from the Truffle Searcher Hut, which is a wonder of the world. Wonders of the world are rare and special production sites which can only be acquired from assembling card pieces (they usually take 40-75 card pieces). You can check to see if you have any pieces yet in your card piece inventory - they are listed as level 5 card pieces. You can collect them from booster packs and friendship star cards, and of course you can also trade with other players to get them.
If you're only starting out in the game, you'll probably want to dismiss the customers demanding truffles for now, since it usually does take quite a while to get a Truffle Searcher Hut together.