Evelynn is a great jungle champion, especially for only 1350 IP. Her passive makes her even greater for ganking lanes from behind. After 6 seconds of taking no damage and not attacking, she will become invisible to the map aside from the actual view from right next to her and to pink wards. She is an assassin who can clear jungle camps very quickly with her Q, which requires very little mana.

For runes I went 9 Marks of Magic Pen. because eventually you will sell your Sorcerer's Shoes and need a little magic pen, even though the Liandry's Torment will give you some. You can never have too much! For Seals, I went 9 Seals of Armor because Evelynn can be squishy when in a 1v1, so the armor will help a bunch. For Glyphs, I went 9 Glyphs of Scaling Magic Resist. I didn't use the regular magic resist because she shouldn't need much early game, and it will be more important later on. For Quintessences, I went full out Ability Power for the sake of doing a little extra damage with your Q and E.

The masteries that I chose are pretty much standard for most AP champs, but she will also have more damage to minions for easier clearing of camps.

(see notes)

Max her Q first because that has an extremely low CD and it will be the most usefull spell you have, besides your ult of course! Her W is great for escaping and getting to lanes quicker, but have one level early on of it should be just fine. Her E is also helpful for clearing jungle camps quick by using it on the stronger creep. Her E will also get spell vamp, along with her Q, for a late game bonus. Her R/Ult is exceptional because it does damage, slows, and gives her a shield depending on how many enemy champions that she hit. It is one of the best in the game.

For spells, I chose Smite, which is the obvious jungle spell, and Flash, which is a no-brainer on most champions, her included.

Pros

Near-Invisible Ganks
Hatred Spikes= faster camp clearing
Invisible to most wards
One of the best Ultimates in the game

Cons

Pretty Squishy before level 6
No CC before level 6
Has to be fairly close for her non ult abilities

Start with a smiteless blue (if your team helps), then get the wolves quickly, then move straight to red. Smite to finish the Lizard Elder, then grab wraiths and check if you can gank to kill. If you need to go back, do so QUICKLY. The earlier you gank, the better chance your team has at winning the lane. Frequently check for gank-ability of lanes and go back whenever you have enough for your next upgrade. Remember to tell your team when you're ganking so they know not to go earlier or later than you arrive!

Just remember to clear the camps often and watch for the enemy jungler to gank your team's lanes. When you have an open opportunity, take their buffs! It will give you AND your team an advantage because their jungler will have to go back for mana (assuming he uses mana) and he won't do the extra damage from the red buff. Help your team take the dragon for the extra gold. More gold = more items = more power. REMEMBER THIS.

Overall, Evelynn is a great choice as a jungler if you are willing to practice with her. She is fairly easy to get used to, but not as easy as some like, oh I don't know, MASTER YI. When she is fed though, she can be a great threat, so keep to the tips I gave you and keep LOLing!