I would not reccomend this guide for people who are not level 30 or the ones that don't have enough playing expirience.
Also if you don't like this style of playing evelynn check out other great AP and AD guides, they might work much better for you!
This is going to be a quick but I hope really helpful guide.

Why Hybrid:
Evelynn has AP and AD scaling on her two main damage dealing abilities, and her Hate Spike work really good with Trinity Force. So since mix of physical and magic damage is harder to counter, so I find hybrid way really strong.

Why not:
Hybrid build is more costly than either AD or AP but can still do more damage, so don't go for it if you are no fed! After Trinity Force if you are not fed (doing much better than the rest of the players) just buy Bloodthirster. That would be the AD build but some times you just need to do it!

What is your job:
Gank as much as you can and get alot of kills since evelynn needs alot of gold. Since evelynn has amazing snowballing potential try not to waste it early on!
In team fights just try to hit everyone with your ultimate so you can get that shield, find their AD or AP carry (depends on who deals more damage) and beat the **** out of him! Your lifesteal, spellvamp, shield and Guardian Angel will keep you in life probably long enough to take down both carries.


Items:
Mobility Boots - You really need that movement speed for ganking every single lane and still killing your jungle camps.

Wriggle's Lantern - Amazing starting item. It gives you everything you need early on!

Trinity Force - Eve is lacking CC and slow from this item does the trick. The proc. that deals 150% of AD works amazing with Hate Spike, so you are going to have a lot of those and deal TONS OF DAMAGE! Mobility and AS is just and amazing bonus that you get with this item.

Hextech Gunblade - This item is pretty expensive but it provides A LOT of damage and A LOT of sustain. This is what makes this item hybrid combined with Trinity Force. It also has an amazing active that will help eve a little bit more about sustain.

Guardian Angel - Will keep the focus of you for a little bit more combined with your potential 1K shield from Agony's Embrace. And if you get focused it will keep you allive as long as possible .

Last Whisper - This will make you deal more physical than magic damage, but you will still deal much more damage combined overall. Void Staff wouldn't work because Trinity Force proc. is physical damage.