This is my first biuld so be nice please :]

In this guide I will be talking about Evelynn the Widowmaker
It will explain how I use evelynn as an AP damage dealer.

For runes I take Greater mark of Potency x9 Greater Seal of Alacrity x9 Greater glyph of Potency x9 and Greater Quintessense of Alacrity x3 I chose these runes because it increases Evelynns attack speed alowing her to use Malice and Spite even more effectively and Ability Power so that both Ravage and Hate Spike completely decimate the enemy champions.

For Masteries I use 21/0/9 taking Ability Power Cooldown reduction Attack Speed Attack damage and Armor/Magic Penetration. I take Ability power because it increaes effectiveness of Ravage and Hate spike. Attack Speed and Attack damage because it increases your ults effectiveness. Then I take Armor/Magic Penetration to bypass some of the enemies armor and Magic resist. Next grab Phage and Sheen to get Trinity force which gives just about everything. Finally grab another Sheen and then Lich Bane. I like to get Mejais first but you can easily switch around Majais and Boots of Mobility by taking boots of speed and a couple Health potions instead of amplifying tome. If you would like you can trade Lich bane for Hextech Gunblade but overall I would recommend this set up of items

Everyone has their own style of item build, but I personally like to have Ability power and Attack speed. For starting items I take Amplifying tome and a health potion. After that I get Mejais Soulstealer for AP and at 20 stacks cooldown reduction. Then I move on to movement speed taking Boots of Mobility so that you can get around the map faster. Gaining attack speed and cooldown reduction with stinger and then Nashor's tooth. Blasting wand and a amplifying tome to build into Rylais crystal scepter for survivability (Health) and Ability Power plus a slow.

Skill sequence is a very important part for any build. To get some damage output early i like to get Ravage and build that up as fast as I can because it will be your main initial damage output. After I have maxed Ravage Hate spike is the next one you want to max but by that time you will be maxing both Hatespike and shadow walk so it doesnt really matter. As with all champions upgrade your ult every lvl it is available.

For summoner spells I like to take Ghost and Teleport so that I have a great chase with my ult and and ghost and so that I can get around the map faster i take teleport.
Teleport can easily be switched with ignite or flash. and same with ghost if you want to take flash and ignite as your summoner spells those are both great alternate spells. But mainly I like to stick with ghost and Teleport.

So in summary this build will create a devestating AP damage dealer out of Evelynn. Items will build up your AP, masteries will biuld attack speed and cooldown reduction with Magic/Armor Penetration. Runes will make you even more devestating increasing effectiveness for all of your skills, and Summoner spells making you practically be everywhere at once.
Thanks for reading my guide and please comment :]