How do I deal with decks full of creature removal, direct damage, and counter-spells?

I keep running into these even in casual play and I can't find any way to deal with them. I've tried to only cast spells when they are tapped out, but that rarely works because they don't tap out if I don't cast any spells. Even if it works, they just kill my creatures with direct damage on the next turn.

It's incredibly boring and frustrating to play against because the entire game consists of them just saying "no you can't do that" to everything I do followed by "here's a game-winning card." What are the counters to this kind of deck, and how does a newbie build one for cheap?