Pros:
Good Ganker
Good Burst Damage
Stun
Stealth
Fast and very good at getting around the map
Very Good with good teammates
Very Fun to play!

Cons:
Squishy
Hard to master
Need good timing and placement
If you have a bad early game it is hard to come back

Runes I use, probably not perfect but I like what they do for me:

Armor Penetration Marks
MP/5 per LeveL Seals
Ability Power Glyphs
2x Ability Power Quints and 1x Magic Pen Glyph

I like using this setup as when you are lower levels your abilities will hit pretty hard and it makes ganking easier. Sheen and the AP runes will give you a nice starting burst damage on your E and Q.

I run 21/0/9 and use Ghost and Ignite. I found those together make the best combo. You could even use Exhaust instead of ignite. I tried flash on Eve and I didn't like it as much as ghost. I would say the best is to have Ghost and either ignite or exhaust. I haven't tried teleport or any other skill. These 2 have been very good to me.

Q = Hate Spike (spam), W = Shadow Walk (stealth/stun), E = Ravage (burst), R = Malice and Spite (ultimate that is very helpful in killing multiple people)

I start with Q first to help get some first hits on minions, follow that with W so you have it ready for a kill. Then another Q at 3 and E at 4 around this level I will try and get a kill. I have a decent burst with my stun and E followed by Q spam and ignite. Leveling your E up is nice as it does very good damage early/mid game. It helps to have Q at level 2 also for some decent damage as well and it makes last hitting a lot easier. Get R whenever you can and remember R > E > Q > W. I prefer to get a 2nd point in W around level 9 so the stealth lasts longer and the stun as well. After that I level it last. You can also try other skill sequences, but this is the one I found to be the best for me and my playstyle.

I start with a Sapphire and 2 HP pots. I finish Sheen first, and then buy Boots of Mobility. Once you get those 2 items you are a pretty good killer because your sheen will proc from spamming Q and so on. After that I buy Trinity Force which gives you some nice damage as well. Follow that by a BF Sword and here is where I tend to buy different things depending on how the game is going. If I feel we are doing fine and I wanna do more damage I will buy Bloodthirster or Infinity Edge or even Black Cleaver. If I feel I need some defense I will buy Banshees Veil or Guardians Angel. Games usually end around that time. If they don't then just buy accordingly its pretty easy to know what you need. I usually only buy one defensive item and the rest damage. If you need you could build a madreds blood for those high hp targets that require it. I haven't had a game go long enough yet to where I had one.

When farming just spam Q to kill minions and last hit. It helps push lanes faster and when you are killing turrets don't be afraid to pop your ultimate as it will give you a boost to attack speed and help kill turrets much faster. Try and get the lizard buff as it will help when you gank to give that extra damage and slow. I tend to not worry about minion kills. You gank a lot and that will help with your money. You will also slow them down a lot by making them by wards and oracles.

Playing Eve is simple as you try to pick off squishy champs or champs that are overplaying. I tend to pop stealth run in ping for teammate and stun them, followed by your E, then R, and then Q spamming and throw in ignite if needed. One thing you want to watch out for is getting caught from Oracles or Wards. Be wary of what your opponents are buying. You are very squishy, and CC can hurt you. In teamfights I prefer to let everyone engage then I pick off the focus fire target. People think Eve is a horrible champion, but if you watch an eve who knows what she is doing she is very good. She is also a good counterjungle character. From time to time do not be afraid to check the jungle if they have one and try and find him. Sometimes you can pick him off and even steal buffs. I have multiple times stolen dragon, blue, and red buffs from an enemy jungler and even killed them. Know jungle routes and try and just think where they would be, even if you check and they not there it is fine. Set up wards in enemy jungle and then set up ganks. Just be patient with her and watch your enemies closely. Make sure you communicate with teammates to perform ganks. Eve is also good because she makes the other team use money on pink wards and oracles. They end up spending a lot on those which will keep them weaker.

My last 5 games played with her are:
26-8-7
10-4-16
6-4-1
13-5-18
7-4-14

Also don't worry about what people say before games start. People are always nay saying Eve and if you play her right they will quickly stfu you know!!! People love to talk **** to you after you kill them also, so just be ready for a lot of QQ!

Leave me comments on what you think or how you did. Try the build first before you hate on it please. I am trying to make it better as it is obviously not perfect! So any feedback is greatly appreciated and welcomed!