Welcome to my guide on jungle Evelynn.
You will find many helpful tips and hints within to play and master her.
Please note that this guide features the AD Evelynn and not the old AP one.

I added a non jungle Build if you're not that familiar with jungling.

You may notice the 2 Greater Quint of Intellect im using in this build. These are a must have. You don't have enoug consistent Mana to cast Hate Spike all the time during jungling without having these quints. But they aren't a waste neither. Evelynn still has high Mana cost lategame and these 2 will help you alot.
The third Quint is a common Greater Quint of Desolation

For red runes I put in common Greater Mark of Desolation to shred through enemy armor (note that this guide features AD evelynn since she is much more viable)

Yellow runes are Greater Seal of Armor to decrease the damage done to you by Minions in the jungle. (You need them!)

I use the blue runes Greater Glyph of Attack Speed to increase my personal damage output and clear the jungle faster.

Jungle

Very mixed masteries you will need for a successful jungle Evelynn.

12 points in offense:
Deadliness 3/3 - increased crit chance is always good
Plentiful Bounty 1/1 - decreases your smite cooldown and gives a very small amount of gold
Sorcery 4/4 - decrease your cooldown by another 3%
Offensive Mastery 2/2 - increases damage done to minions. Important!
Sunder 2/3 - shreds through enemy armor. Not needed but gives some damage

10 points in defense
Resistance 3/3 - increases magic resistance. Very important for lategame!
Hardiness 3/3 - increases armor. Very important for your survivability
Evasion 2/4 - increases dodge (just needed to get down in the tree)
Defensive Mastery 2/2 - decreases damage done to you by minions. Important for jungling on Evelynn

8 points in utility
Good Hands 3/3 - decreases time spent dead! Always good.
Perseverence 1/3 - ALTERNATELY: If you pick Ghost as your second summoner you should put this point in Haste
Awareness 4/4 - Increases experience gained. Must have

Play Video /league-of-legends/ability/hate-spike-93 Gank!

Evelynn is one of the best gankers IMO!
Because of her Shadow Walk enemies can't see you coming unless they spend their money to buy Pink Ward or an Oracles.
Plus if you have Red buff they won't escape (unless they have Flash) to your double slow

The process of ganking is also very easy since you don't have to mind that the enemy may see you

My personal skill sequence is R>Q>E>W .
I really like the Hate Spike damage over the "burst" of Ravage. Just spamming Q also activates your Guinsoo's Rageblade and you attack much faster.
2 points in Stealth are also more than enough for early scout -and ganking since 20 sec are all you need.

I like to take Flash and Exhaust so that I can duel with strong meele Burst-type champs and still have an escape with Flash+ Shadow Walk

Other good choices are Ghost and Ignite

Evelynn has some very nice additions for your team
1. You can scout the enemy movements and prepare your team for the fight
2. You can backdoor the enemy team and kill their squishies -> flash out and get into stealth
3. Evelynn is also a pro in baiting the enemy team to yours :)
4. The enemies have to spend lots of gold by buying Oracles and Pink Wards to reveal you! + for your team

Pro
-Insane burst damage
-Awesome ganking thanks to Shadow Walk
-Hard to reveal
-Underestimated

Cons
-Oracle is hard counter
-Counter jungling f*cks her up
-Average jungling

But afterall shes fun to play and I hope you guys enjoy :>