Welcome to the Evelynn Stealth Academy. To begin with, I've played Evelynn since season 2 when you would get flamed for just selecting the champion. I've tried many arrangements of item sequences and found this one to be what most often brings me success in league of legends. I strongly believe that other builds and even using some unconventional items can bring out the versatile quality of Evelynn that I've found when playing her. Meta exists not because it is the right way to do things, but it's the most effective especially for those who are in positions where they will be on equal or less footing with regards to their skill on the rift. So take my advice with a grain of salt and I will try to omit the obvious while providing a comprehensive aid in mastering Evelynn.

If you can get your allies to give you a smiteless first camp or to leash you red do it. If you get red buff as your first camp it may be profitable to gank top early or kill the enemy jungle.

In most situations while its a risky option you will want to go straight to either Chickens or Wolves after you get leashed Rocks or Golems, then kill Skuddle. This will give you a lot of free hp that is useful in getting the next camp.
If I feel that the enemy jungle is more of a passive type or if im feeling lazy my standard first clear is as follows.

Rocks-Chickens-Skuddle-Red-Rocks again.(Rocks will spawn again right about the time it takes to do all of the rest and get to their spawn area.)
Always smite the first rocks because the stun will help you kill skuddle.
After either a quick gank or clearing the small creatures from another camp I go to the fountain and proceed to the next skuddle while the rock buff is still up. Or if I decided to smite red for the health and gank ill back, then start with blue buff.

In order to get all monsters to be damaged with q you have to get them to chase you a bit. This doesn't work so well with blue because the small monsters are slow but for the rest of the camps, if you hatespike then back up a little the small creatures will rush to you and the large creature will be behind them allowing you to damage all of them at once.

Blue/Red Buff---Its important, at least for the first 2 clears, to use E right after an auto attack(to use it while that auto is on cd) and after that only auto 4 times to make use of most of the attack speed buff duration while also avoiding the large monster to attack you an extra time when you back up and kite it until your E comes off of cooldown. If you can kite it around and q the monster without reseting it you are saving enough health to do extended clears like the one explained above.

I usually only do this for the blue buff, if I have blue buff, or if im about to back, because the mana used from using Q that many times is most of the mana-pool.

Play Evelynn, wether you try this build or not, ****it. Ill add more wall of text as well as different things to give this guide a more easy to read feel soon. GL HF