Elise the spider queen, she's somewhat different than other mages, I found her difficult as i bought her but she's fun to play if you know what you're doing, despite the AP carry role she's not that good mid but does very well in the jungle thanks to her skills.

Pros:
-Fast jungler (spiderlings=extra damage, bonus magic damage in spider form)
-Good ganking ability Reppel
-Not bad durability
-Healing skill in spider form
-Good escapist
-Excellent in finishing off low hp foes
-Spider form spells has no mana cost


Cons:
-You can't really run with your E when there is no creep to jump on
-No CC in spider form
-Need to watch your CD on spider/human form, because CD can get you killed
-I find her hard to master, she's deffinitely not an easy champion
-Lack of damaging skills (oh come on 2 in human form and 1 in spider form is not too much...

I focus on jungling with armor seals and marks, with addition of ability power, it makes sure you're jungle is quiet fast and effective as you don't have to go back to base till like lvl 6/7. I recommend that build although if someone is afraid of magic damage should replace some AP with magic resist.

Masteries are pretty simple as for jungler, not need no explaination.

As for items I found Hextech Gunblade incredibly useful on elise, works great with her w, gives her some more damage which is significant in spider form as the only source of damage is your q and basic attacks, yep Hextech Gunblade helps a lot you should take it asap. Then rush for Rylai's Crystal Scepter cuz slow always help, especially that The Spider Queen, even in her spider form isn't as fast as she should be. The rest seems pretty obvious, Rabadon's Deathcap for more damage, Guardian Angel for some nice sustain ( combined with E in spider form can really save you, Nashor's Tooth great attack speed, great mana regeneration and great Cooldown Reduction, fits Elise nice, if you're doing good, pick it before Rabadon's

Other items you might use:

Lich Bane some extra on hit damage never hurts, speed boost is also nice
Abyssal Mask If you have troubles taking down mid laners go for that
Frozen Heart Viable but i prefer GA + Nashor's
Zhonya's Hourglass You kinda have that with your E in spider form so it's waste of money if you ask me

Spider Queen- your passive, anytime you cast a spell in human form Elise is preparing a spiderling that follow you and attack foes when you switch to spider form.

Neurotoxin / Venomous Bite- this is the key of switching form, you should begin with human form and neurotoxin as it takes some damage +8%+ 1%/50AP of the targets current health but in spider form it takes some amount of damage + % but based on the lost health, taking down the low health foes, MAX it second.

Volatile Spiderling / Skittering Frenzy- your main source of jungling, helps taking down creeps fast and gives some nice regeneration in spider form, in human form pretty much like Maokai's seeds except that it goes straight ahead and then goes to a nearby enemy or blows up after 3 sec, MAX it asap.

Cocoon / Rappel - in human form it's a skillshot that stuns first foe it lands on for 1,5 sec, in spider form Elise climbs up and then if used on foe she drops herself and her spiderlings on him, if you used it on an area you can use it again to jump on a foe too, however you will land in the same place where u used it when there is no enemy to jump on, what's useful about it it's that you can scout area in range of the spell which makes it pretty useful. Important!: always use this when enemy champion dives you under your turret, just make sure he hits you so turret can target him, you disappear, let the turret land hit or 2 on your enemy and then you just jump on him to finish off, pretty damn useful especially early game.

Spider Form / Human Form- switches Elise between her spider and human form, my recomendation when you start a fight, do it in human form, deal some damage then switch to spider to follow your foe till he's dead. Note that spider form gives you bonus speed, magic resist and armor.

Smite jungling must have.

Flash i use it myself and it fits me best, although you might like Ignite / Exhaust better

You should always start with blue buff, then go through the wolves to wraiths camp and red buff then golems, by this time you're already lvl 3 so you can gank bot lane easily, don't do it before lvl 3 because you'll probably just fail... even if you grab a kill or assist, continue jungling and ganking other lanes untill you have some money for boots and hextech revolver.

Elises role in team work is pretty obvious you always need to find your squishy target, AD or AP carry, if they dont have much resist and they usually won't you'll grab an easy kill. Start in human form, throw stun, release volatile spider and use your neurotoxin before spider hits, then switch to the spider form and follow with venomous bite, if he/she flashes or something use reppel to continue the chase. Choose your prey wisely, go from behind to catch carry off his guard.

I like Elise a lot and you should too! She's different than standard AP or standard junglers plus she's a freaking spider, unless you're arachnophobic, you'll find it pretty cool.