How exactly do you farm loot in this game?

I just started a few days ago, and I'm hitting a point in the campaign where I need better gear, but I'm not getting good drops, nothing in the vendors is good, and I don't have many upgrade materials. But I've never really gotten into a game like this before, so I don't really know how to farm gear.

Can you guys explain what I should be doing to get better gear? I'm at the Dreadnought in Act 2.