Eve is an incredibly item-dependent hero, I find, so you HAVE to ensure that you either get farmed or get kills. If it doesn't look like you can get kills, then you need to focus on farming. That said, I am not an expert on Eve, but I prefer to build her with Trinity Force, either Sorcerer's Shoes or Merc Treads, depending on how I feel, then go for Bloodrazors. Her ult has HIGH attack speed bonus, so you'll rip apart anyone who you open up on. Throw in some lifesteal to build into a bloodthirster, and then an infinity edge if the game goes on, and you'll be fairly powerful.