This probably will not be that informative for seasoned Elise players, but I happen to be trying to improve my play with her, so I'm using this space to write down things I've discovered/learned/re-learned.

Re-learned? Yeah. I played Elise a decent amount before her most recent "re-work" and some things about her have changed. Not in huge ways pre se, but changes in skill ordering, item builds, and combo rotations are worth debugging in a custom game even on your favorite champs. Go find a good guide or video on them and see if you are doing things in a way that makes sense given the current state of the game.

Volatile Spiderling / Skittering Frenzy

Case in point. I just read the description of her abilities and I got reminded (I did read this in the patch notes, but I was still thinking her sustain came from her E) that Volatile Spiderling / Skittering Frenzy is no longer the source of her health sustain. That has been moved to her passive, Spider Queen.

For some reason I never realized that while in spider form, none of Elise's abilities cost any mana. So hey if you want to stay out in the jungle a little longer just stay in spider form and you can clear another camp or two before backing.

If you need to clear a minion wave fast, you want to walk into the middle of it and unleash Volatile Spiderling because then the AoE will hit everything clustered around it. If you send it at the cluster of minions and there is an odd minion in the way, it will explode and only do damage to that out of formation minion.

Supposedly if the Volatile Spiderling is skittering around when you transform and target something with Q, Venomous Bite, the Volatile Spiderling will also leap with you guaranteeing that it hits what you've target, but I haven't gotten this to work reliably. (Anyone know how to guarantee this happens?)

Spider Form

Gives you +25 movement speed. Use it for traveling around the map faster.

Scuttle Crab

With Cocoon to reduce its defenses, Elise kills this thing quickly at all stages of the game and you gain health back from it without losing health in return, so kill them pretty much every time they are up for the vision + speed shrine, XP, and bonus gold.

Standard Ganking

Generally you want to gank in human form.

So scurry to the lane in spider from and ping the gank target so your laner can be prepared for the gank. Then transform out of vision range of your target to ensure that R is off of cool down for the later stages of the gank.

Walk into lane. If you have Red Buff. Auto attack them once to slow them. Then hit them with with E, Cocoon, fire off W, Volatile Spiderling, at them, and then hit them with a Q, Neurotoxin.

So AA + E + W + Q (without Red Buff you can skip the auto attack).

Next transform into Spider Form via R and jump on them with Q, Venomous Bite. Then activate W, Skittering Frenzy and dish out as many auto attacks (AA) as you can.

If they Flash or dash away you can follow them with E, Rappel and finish them with Q when it is off of cool down.

So R + Q + W + AA + E (if necessary) and finish with Q and as many auto attacks as it takes.

Between you and your laner they should be very dead or at least headed back to base to recover. If their Flash is down be sure and make a repeat visit to the lane in the next 5 minutes if the flow of the game allows for it.

Tower Diving

I'm still working on perfecting this. Ideally you want your laner to help you and a minion wave at the enemy tower to take tower aggro. Try and get in position behind them to pencer them between the threat of yourself and your laner which will cause them to hug their turret making them easy to hit with E, Cocoon. Then proceed with the ability rotation I've described above. Though in this scenario you will either be using E, Rappel to follow them after they have flashed or to drop tower aggro and let your laner finish them off.

Non-standard, non-tower dive ganking

Sometimes the enemy laner is not going to be in position to get him with a E, Cocoon.

You may still want to try a drive by in this situation. By that, I mean E, Rappel, onto them or to minion near them that gives you a reasonable angle to hit E, Cocoon. This will quite often result in them blowing a Flash, which gives your laner a significant advantage over their lane opponent. (Successful ganks give your laner an advantage in lane. This doesn't always have to be a kill). Blown flash = successful gank.

Cocoon / Rappel

While in spider form you can use Rappel to dodge a lot of spells. Fizz's Chum the Waters is a good example.

If fleeing you can also use Rappel to come down on enemies or neutral monsters.

If you need to get back into a fight quickly after dodging a skill shot you can just reactivate Rappel to come down in the spot you started from.

You are probably going to get yourself killed a time or two by accidentally clicking on a target initiating the drop back down portion of Rappel prematurely. Keep thy finger off the E key and avoid clicking on anything as well if you want to stay up for the entire duration of 2 seconds.

Sometimes you are going to do everything perfect and your team will be dead and when you come down there will only be enemies to great you. Hope you have Zhonya's Hourglass by that point so you can live for 2.5 more seconds.

Clearing camps

Elise can clear the entire jungle with just the two health pots and the health sustain she gets from her passive, Spider Queen.

Start with W and start the camp in human form. At 1:52 fire off Volatile Spiderling. Smite and AA the largest creature in the camp. Then hit R, Spider Form, to turn into a spider and activate Skittering Frenzy to increase you attack speed and the attack speed of your spiderlings. Attack move/orb walk/animation cancel away from you spiderlings. They are going to die. In fact the large buff monsters will kill them in one auto attack, however that is an auto attack that will not be aimed at you so rejoice. You are the queen, they are the minions, it is their job to get squished instead of you. AA the camp until it is dead. Put a point into Q Neurotoxin / Venomous Bite. Walk to the next camp. If it is far off stay in spider form. If it is nearby say Gromp to Blue Buff you can transform into human form and walk over so that spider form is off of cool down when you get there.

Now do W + Q + AA + R

Neurotoxin travels at a faster rate than Volatile Spiderling so we open up with Volatile Spiderling, but we still do the % current health damage of Neurotoxin first as that maximizes our damage. You can auto a time or two before the big creep gets to you before switching to spider form if you want. (I do this if Spider Form is still on cool down).

When in spider form, Q the large creep, and then do the orb walk thing so your spiderlings tank the damage from the camp creeps. Activate Skittering Frenzy and proceed to auto attack the camp to death. If it is taking a long time to kill the camp and all your spiderlings are dead you can switch back to human form and hit the camp with two spells which will give you two new spiderlings to help tank the camp once you switch back to spider from.

Elise is a good early ganker with Cocoon, so after taking you first buff, I recommend having a point in all three of you main abilities in case you see a good opportunity on the map.

If you have blue buff you can Cocoon the biggest creep in the camp to get a few more autos off on it from range while it is stunned. I don't really recommend doing this on anything except the Scuttle Crab until you've got your mana sustain fixed with something like Enchantment: Runeglaive.

Thems the basics.