Expert Spider Solitaire (as the name would imply) is extremely challenging, and recommended only for true solitaire champions.
Just like regualr (and "Hard") Spider Solitaire, Beat Expert Spider Solitaire by removing all cards from the game. You do this by stacking cards of the same color into "completed" piles (King to Ace). Similarly, you must avoid stacking cards of differing suits, because it will cause the above cards in the stack to go inactive.
Expert Spider Solitaire players will be quick to flip as many cards as possible in the tableau--even sometimes at the cost of stacking cards of alternating suits. Though this is typically not recommended, it is often a necessary evil in this strategy game to avoid having to click the stock button too soon--which will almost assuredly cause most (if not all) of your stacks in the tableau to go inactive.