Give 'em a nudge. Is your opponent intentionally stalling, or slowing down the game hoping to make you quit? Watch for the Nudge button to appear. By clicking it, you'll force the other player to make a move, or be disconnected from the game.
Watch your partner. If your partner starts throwing away high cards ("ducking tricks"), it might be to avoid getting stuck with overtricks and bag points. But if your partner plays a high card which then gets trumped by an opponent, you might need to help cover some tricks.
Horde trumps. Having lots of trump cards means you'll have extras after other players have run out, and this might result in extra tricks you can take. Remember, the Ace of Spades is a guaranteed trick.
Ace in your pocket.
Aces in other suits are also likely to take tricks, especially if played in the first round of that suit. Once a few rounds have gone by, players are more likely to be out of that suit, and can then play trump.
Take one for the team. If your partner bids Nil, you'll have to take all the tricks for your team. Lead with high cards. If your partner runs out of a particular suit, lead with that suit to give your partner a chance to ditch high cards from other suits.
Know your Nils. If an opponents bids Nil, lead low to force the player to take a trick and a penalty. Watch for suits the Nil player is out of, and avoid those. Whenever possible, deny the Nil player opportunities to discard high cards.
Refresh your memory. If you're forgotten which cards were played in the previous trick, click the Last Trick button to reveal them.