eve is a very good carry/assassin. this build works best when no one on the team jungles... this is a very fun build that I use as my main but it is just a guide and not all items are always the same. (i.e. tank heavy might sub in L.W. or madred's.)
AD eve is, in my opinion the best way to play her. eve was intended to be played ap but she is simply too weak to utilize her ap skills. her ult is the prime example of why she should be played ad, esspecially since it refreshes every time an enemy champion is slain.

the rune setup is pretty standard for a physical dps champion with armor pen, attack speed, cdr for hatespike,stealth, and Ravage cd, and mana because eve is very mana hungry especially mid game. I like to have two health quints because she is squisy and the extra health really helps esspecailly with golem at lvl 5/6

shadow walk is a great first skill because the enemy usually thinks you are jungling and you can set up before minion ganks. it is important to get hatespike to lvl 2 for golem and it also helps with dps in ganks. ravage is a skill that is important for golem and ganks as it reduces the enemies armor. but overall i just kinda go with the flow and get what seems right and is needed.

I start with boots of speed because they help get you into the action or out of trouble early game, it also allows you to get two health potions and a mana potion. conserve your mana till lvl 5 when you can get golem(use the potion after you push your minions away from your tower a little, before going for golem. get sheen asap because it gives you a lot more damage output early. jungle and or gank till you can buy boots of mobility. now you can run all over the map super fast and can get ganks with ease. with boots of mobility if you cant quite get the kill keep chasing but dont attack with your q, instead go stealth and your boots will kick in soon and you can catch up with ease/stun/kill. finish off triforce. then get bilge water cutlass and then gunblade because this will add a little bit of damage and slow enemies. after that get rageblade as the added ad, ap, and as will increase your damage output, you gain full stacks super fast and you attack speed skyrockets. next get BC and by this time the game is usually over. but just for kicks I added BT or PD.

so all in all i really like this build and eve can have a huge damage output through her amazing attack speed. she becomes so fast late game that even with oracle the other team is not able to see you till its too late.
please rate and comment, but please try it out first before you get too hypercritical