Typically, this is something that you aim to solve in the deckbuilding stage. The big idea is that all the discard in the world can't save your opponent from the top of your deck. If you're on a highly synergistic or combo-based deck, discard is going to be a huge beating against you, but you can try to throw Leyline of Sanctity if you don't want to switch to a strategy less dependent on synergy. If you're playing an aggressive deck, often all of your cards roughly do the same thing so it usually doesn't matter that much that they take 1 or 2 cards from you, you just continue to smash in. If you're playing a midrange deck, most of your cards are high impact, so you are pretty happy to play off the top of your deck. The fact that you can't easily play either of those archetypes right now is a different problem, since the meta in Standard is just broken.
With all that said, the best way to play against discard right now is to just play Veil of Summer, which is an enormous blowout against the discard deck.