When Elise came out, she always used to be a perfect jungler. Her cacoon(cc)and her burst ap damage will put an enemy opponent to the ground, Even by building her So tanky and Giving her an item for example Liandrys torment she will do insane damage and be tanky as hell.

At the start of the game you should always start with hunters machete and 5 pots so you could get buffs and killing minions easier. I will always prefer for every jungler to gank top at level 3 so you could camp mid or bot. By getting First blood on top lane you will have a huge advantage and never forget to always give First blood to your ally, even if you have 0 kills, assists count. Get Spirits and haunting guise so you could get good hp and good damage. If your low in cash and you hardly getting around 1k gold I prefer for you to go locket(Never forget to tell your support that your building locket, 2 lockets wont work its unique passive), but if your having good cash and getting kills late, i prefer to get either Sunfire or Visage depending on the champs. Always be smart , never follow my build continuously. If an enemy AD opponent is really fed, do not build Visage, build sunfire or randuins(depending on the enemy AD opponent's Attack speed is low or high), If AP opponent gets fed, better getting Visage. If your team got no tank, its better to go full tank and only get liandrys so you initiate in team fights.
Best Elise Recommended items:

Spirits of the Ancient golem(After getting full build, sell this item and get warmongs)
Sorcerer boots(upgrade it to homeguards)
liandry's torment
Locket of iron solari(if support goes Lockets get sunfires,randuins, or visage depending on the enemy champ)
Rabadon's deathcap
Rylai's(ONLY and Only if your top laner and your support are tanks) or Banshee's Veil

Always remember Full tanky+ liandrys(if and only if your team was filled with Damage instead of being tanky), Only build 1/2 Ap 1/2 Tank if and only if your top lane and support were tanks.
Never stay in the jungle killing creeps for so long, always gank as fast as possible, and don't forget lane ganks and also get Pink wards so you could destroy enemy opponent sight ward and gank him.

Runes Should always be Ap so you could damage to your opponent. Even by going ap you will still tanky and so powerful. Never get Movement speed runes or Attack speed runes because you will always have your spiders (w).

Never go full tank masteries or you will be so useless early, So its better to get full ap masteries so you could do really good damage early and late. Don't worry if your going to die fast, you can always building tanky items.

Never max your W 1st even if it does better damage then Q, still max Q so you can harass hard( Q is not a skillshot, but W is)

While jungling Always start with red( If blue side), start blue( if purple side). After getting red go immediately to blue so you don't get counter-jungled. always look for top if the enemy team got wards..so you could get pinks and gank. Never ever stay alot of time jungling...always be a fast ganker.

Being a jungler you should carry your team to victory. Grouping as 5 and getting dragon or baron is alawys better than seperating and letting your enemy team to initiate your teamates. Never forget to pop your locket of iron solari in teamfights.