Elixir's price is raised however I still think that it is viable option for Zed. It is usually quite useful when you can bait the enemy's ignite. For me 1 health potion is usally enough but if you want you can go for 1 elixir and 3 health potions.I get dorans blade as first item because it gives you good amound of damage and hp. Vampiric scepter is my second item because it really helps me stay in lane way longer.I go for brutalizer to prep up for black cleaver. Blade of the ruined king is definetely and item you should take it gives you great amount of sustain and it helps you chase down and enemy or run away from one. I get bloodthirster so that i can have enough damage to burst the enemy adc or apc down really fast. Last whisper helps you melt down the enemy hard. I get cd boots so that I can use my ultimate any time I want. I get warmog so that I can survive more in teamfights and pin down the enemies

Until you get to level 6, just farm hard and try to poke the enemy. When you get your ultimate go for the kill, you will either kill him or you will force him back which will give you the farm advantage.