Don't Draw From the Discards Unless it Completes a Run
Drawing from the discard pile has two disadvantages. The first disadvantage is that you are passing an opportunity to see the top card of the deck, which might complete a run for you.
The second, and bigger, disadvantage is that your opponent can see what card you take from the discard pile. If you pick up a seven of clubs to match the seven of diamonds in your hand, you may never get that third seven because your opponent will hold onto it until the end of the game.
Watch Your Opponent's Draws From the Discard Pile
If your opponent is foolish enough not to follow the above tip, you can gain an advantage simply by holding onto cards that your opponent might be trying to collect. If you are deciding whether to discard a six of clubs or a six of diamonds, and you saw your opponent pick up a seven of diamonds, you should discard the six of clubs first.
Pay Attention to What Cards Are Being Discarded
In some cases, this can give you information about an opponent's hand; cards close to what your opponent discards are usually safer to throw away.
The biggest benefit of paying attention to the discard pile is to be aware of what is left in the deck. If two jacks have already been discarded, your pair of jacks is never going to become a meld, and you should get rid of it.
Discard Higher Value Cards Rather Than Lower Ones
You'll eventually want to be building towards a hand good enough to knock with, which means you need to lower your deadwood score. A single deadwood face card means that all the rest of your cards must be melded to knock, and even then it would be a very weak knock.
Dump your deadwood face cards and hold on to low numbers, to increase the chances of an early knock.
Your opponent, in accordance with the above tip, may discard some high cards early on, and give you what you need to complete a meld. As the game continues, the risk of holding deadwood high cards increases, and you should probably dump any deadwood face cards by the time the deck is halfway gone.
Knock Early When Possible
There is a possibility that the other player will undercut you, but if you knock early enough, you are likely to catch your opponent with enough deadwood that you can score. Even knocking with 10 deadwood points, early enough in the game, can be very strong.
Don't Make Weak Knocks Late in the Game
If the deck is more than halfway gone, your opponent has probably gotten rid of the worst deadwood, so knocking with 10 points is an invitation to be undercut. Remember, the longer the game has gone on, the better your hand should be to knock.