Intro

Hi, I have played Elise around 400 games.
This guide will be mostly useful for B, S, G. If you are P or higher, you may want to just look at runes and masteries.
I think Elise will be more nerfed she is still too strong.

Pro:

Fast Jungle
Burst Dmg
% Health Dmg makes her a decent late game champ
Stun
Gap closer/ Escape skill

Con:

Can be squishy
No "ult"
Her skills use a lot of mana (after blue is gone and before Spirit of the Spectral Wraith, you may be mana-less.)

My View of Elise Jungle

Jungling:

★★★★☆ Really Fast but early jungle is not the fastest. Udyr, Shyv might be faster.

1v1 in Jungle:

★★★★☆ Elise can beat everyone (same level, health etc.) except Olaf/Shyv/Shaco with ignite (assuming you hit your stun).

Ganking:

★★★★ really strong gank but the caveat is that you have to hit Cocoon to be a strong ganker. However, even if you miss Cocoon, you still do a lot of dmg so you might still get a kill.

2V2 at top or mid

: ★★★★★ Really good 2v2 as long as your have Rappel, you can take some dmg then Rappel then come back then for the kill with Venomous Bite.

Team Fight:

★★★ Not the best team fight. However, you can still have some impact with your stun. What you want is you want to be tanky and you want to stay between their dmg dealers and your team. This scares their adc/mid to deal dmg to your team. If mid/adc come near you then stun and do your combo then back until your cd is up. You can also stay near your adc to protect your adc if your adc deals more dmg than their adc.

Overall

★★★★, one of the best junglers in the game atm (along with Lee, Eve, Shyv).

You can also go 9/21 but I like 21/9 for fast jungle clear and early dmg. If you are going 9/21, go 3 Sorcery Butcher Feast 3 Mental Force Arcane Mastery. You would go 9/21 if your team lacks a tank.

You may get Greater Quintessence of Movement Speed/ Greater Quintessence of Hybrid Penetration on quints.
I prefer Greater Quintessence of Ability Power because it allows fast jungle.

Other potential runes are:

1. fast jungle runes was used by Korean pro gamers that start with doran's blade but not recommended anymore due to the nerf on Doran's.

Reds: Greater Mark of Attack Speed
Yellow: Greater Seal of Armor
Blue: Greater Glyph of Ability Power
Quint: Greater Quintessence of Ability Power
The fastest jungle clear runes

2.Ganking Elise

Reds: Greater Mark of Hybrid Penetration
Yellow Greater Seal of Armor
Blue: Greater Glyph of Magic Resist
Quints: Greater Quintessence of Hybrid Penetration

3. Cover Elise best for swap lanes

Reds: Greater Mark of Hybrid Penetration
Yellow Greater Seal of Armor
Blue: Greater Glyph of Magic Resist
Quints: Greater Quintessence of Movement Speed

Flash and Smite.
Only choices.
Your Flash-> Rappel or Rappel-> Flash is a really strong gap closer or escape mechanic especially in the jungle.
Flash is really strong on Elise because of Rappel.

If you are planning to play Elise jungle:
Make sure your team has an initiator.
Many times jungler will be the initiator eg. Amumu, Nautilus, Vi, Jarvan IV etc.
If your team doesn't have an initiator, you will have to build more tanky.
Elise IS NOT AN INITATOR, even if you hit stun you have to get so close to the target, not the best way to fight.
Also, make sure your top laner is someone who can do some damage early level.
Elise is really strong early level and if you fight 2 v2 at top, you will likely win if your team laner can put out some decent damage.
You might want to consider banning fast jungler such as Shyvana, Udyr but I don't recommend banning them as there will be other champs that you want to ban.

Full skill combo for max dmg:

Volatile Spiderling-> Neurotoxin-> Cocoon-> Spider Form-> Venomous Bite-> Skittering Frenzy->after they Flash-> Rappel-> Venomous Bite-> Human Form-> Neurotoxin-> Volatile Spiderling-> Cocoon-> Spider Form-> Venomous Bite-> Skittering Frenzy
It is best to use Volatile Spiderling first because it has travel time and you should use Neurotoxin before the spider hits the target.
Also, you should hit your Cocoon last for maximum stun duration when you use your Skittering Frenzy.
This can be applied when you are ganking but most likely you will have to Cocoon the target first then Volatile Spiderling-> Neurotoxin-> Spider Form-> Venomous Bite-> Skittering Frenzy

When you are ganking with Rappel first:

It is important to know where the enemy jungle is if you get counter ganked, you won't have your Rappel.
Rappel on to the minion or the enemy champion, use Venomous Bite if you can; if the enemy is too far, transform to Human Form as soon as you land on the target with Rappel. Hit your Cocoon, Volatile Spiderling-> Neurotoxin-> Spider Form-> Venomous Bite-> Skittering Frenzy. If you miss your Cocoon, they will get away.
It is important to have your Spider Form/ Human Form always available when you gank. Wait 2~3 seconds before you gank if it is on CD.

Buffs + Jungle:

With S4 Buff in the jungle, you don't level up to 3 after doing the double buffs.
Get w and get leash from the bot duo. Use Smite to get the buff. Do wraiths/wolves after your first buff. Then get your second buff. By the time you are at your second buff, your smite will be up.
Make sure you bring the monster into the bush to avoid potential counter jungling.
After that, note your buff re-spawn times and jungle whenever available. Now that you use smite on your first buff, the respawn time is usually 7:08~7:10 if you got bot duo leash.
You want to route your jungle so that after you clear your jungle, you can gank a lane close by.
If you feel that you are stronger than the enemy jungle, you might want to steal the 2nd buff from the enemy jungler. Ward the first enemy buff around 630, use trinket. Also ward bushes near the buff so that you will who are coming, and make the decision to run away if you need to.

Micro-Control

You can micro control so that you and your spiderling won't receive any hits from the monsters. As soon as you see the monster targeting you move back, then the mosnter will target your spider, then move towards the mosnter will target you repeat. But ths requires such intense micro and may delay killing the monster, only do this early game for the first two buffs.

Ganking

Remember that Elise is a strong gank-er + counter gank-er.
However, Elise is weak being counter ganked.
She is only strong when her full skill combo is available so be careful of being counter ganked.
If you ward enemy jungle, it becomes really easy to predict where eneny jungler will be.
It is best to focus mid and top pre six. Many mid and top laners become tankier or get skills that allows them to escape easily after 6. Also, if your top gets a kill, it is really easy to snowball top unless if your top got countered.

Ideal situation:

feed your top a kill or two, let him snow ball. Get to 6 then start focusing bot and mid. At this point in game, you can easily do a dragon with your support so if you can get a kill mid or bot, it almost guarantees a free dragon if your teams didn't lose too much health in the process. After you get your Spirit of the Spectral Wraith, you can do solo dragon without losing any health.

You can solo Dragon

if you have Spirit of the Spectral Wraith; just remember to ward near bushes and pink/lens Dragon pit.

Solo Baron Nashor:

you need lvl 16, Spirit of the Spectral Wraith, Spirit Visage not required but preferred: Liandry's Torment.
When you are soloing baron or dragon you need to use skills then move back so your spiderlings can tank for you. Soloing baron will take a wile about 40~sec.
It is recommended to use Volatile Spiderling first then Neurotoxin so when you transfer back to Human Form both your Volatile Spiderling, Neurotoxin will be up.

Skills: Volatile Spiderling-> Neurotoxin-> Spider Form-> Venomous Bite-> Skittering Frenzy-> Venomous Bite-> Human Form-> REPEAT

Spirit of the Ancient Golem VS Spirit of the Spectral Wraith:

In S3, Spirit of the Ancient Golem was OP as F but in S4 Spirit of the Spectral Wraith is better.
Tenacity + 350 HP VS 50 AP + 8% of spell damage dealt to monsters as Health and Mana.
You can jungle forever with Spirit of the Spectral Wraith and you can solo Baron too!
In Tema fight, obviously Spirit of the Ancient Golem is better than Spirit of the Spectral Wraith. However, if you look at the jungling speed/utility, Spirit of the Spectral Wraith is better. I would only build Spirit of the Ancient Golem if you are really behind or if you need that Tenacity (eg. they have Nautilus, Leona and they are all AD, you would go Ninja Tabi and you would need that Tenacity]].

Itemization:

Focus on getting Spirit of the Spectral Wraith with a Boots.
The mana spell vamp is really good as she can just spam her ability to fast clear the jungle. The spell vamp health is also good feature but she doesn't really lose any hp because spdierlings will tank for her.
Always get two wards and some pots when you go back.
After spectral, if you are dieing a lot, forget dmg, just go tanky and try to farm to catch up and just ward enemy jungle to locate the enemy jungler to warn your team for potential gank. .

What you can get for MR:

In S4, I expect support to get Aegies/Locket.
Mr comes down to three choices:
1. Abyssal Mask: Grab this if you are ahead or if your team has other AP heavy champs.
2. Spirit Visage: My go to item. The 20% CD on this thing is too good. You will end up doing more damage than abyssal over time and also it allows you to solo baron.
3. Banshee's Veil: Grab this if they have teemo, nidalee, blitz
Get 0~3 above items depending on the situations.

Elise is still op play her before Riot nerf her more.
It is possible to carry as Elise jungle in S4. Especially if the enemy is all AD.
Have fun as first 30 games will be really hard if you are not used to her.
Give me any feedbacks good or bad. Thanks for reading.