Throughout the build you may see that I throw in some stats compared to someone at 100MR
I have a spreadsheet going and did the math whenever I use these (I do round for convenience)

The fact is that Elise scales poorly with AP, which makes her trail off a bit late game. She needs to focus on spell pen more than AP to make the most out of her damage.
The only ability that scales remotely well with AP is the W while in Human form (80%).
All the other abilities that scale are either very low percentages or are increasing a % of someones health. Building spell pen will make you scary.

In order to counter Elise with defensive items you have to build MR or Health, (you see where I am going with this?) Her Q in both forms already does %health damage so building health doesn't help too much, so now build MR, that will help all her abilites do magic damage right... then they see that you will penetrate through most of their MR anyway... now what?

This is why I take 9/21 masteries because Elise's bad AP scaling makes the offense tree a bit underwhelming. While the power on her W (aka blinky spider) to harass is nice, that is one ability and it actually levels up pretty well with base damage (For early - mid Game)

The defense tree will help by providing the tenacity we missed from not taking merc treads, decrease the cooldown for everything (always nice when spider form takes no mana...), And make up a little for the lack of straight up tanky items.

I put the point in reducing turret armor because Elise excells at pushing turrets with her W in spider form and this will make it fall that much faster.

The reduced damage and minion damage is so you can afford to be a little more aggresive in lane.
Also the reduced AOE damage: it is likely since you have minions around you in spider form that you will get hit by lots of AOE's so i threw a couple points there

Due to previous explanation (See penetration vs AP) (your choosing between 15 extra AP and an extra 3% damage if your enemies have 100 MR) I Choose Magic Pen Marks and Quints.
You can take AP quints if you really want that early game damage, but to me you can come back in mid-late game so unless your team really knows how to capitalize on early game advantage it won't matter much.
Armor Seals and MR/lvl glyphs because you don't get much defense from this build

(Also you aren't blind obviously so you can go up and hover over the skills to get a description of each ability so i won't tell you what you already know)

Why level R->W->Q->E

R:
Always take points in your ult when possible, duh its your ult... ok a real reason:
it gives you more spiderlings, increases their damage, increases your bonus damage and defense in Spider Form... why would you ever not want this.

W:
The Base damage increase and attack speed increase from leveling this is awesome. It far outdoes the small base damage, and non-champion damage cap, increases you get from the Q.
The more you level this early the faster you can harass with human form = faster into spider form = faster kills. It just makes sense.
PS: the life gained back from using this skill really isn't enough to do anything, for one it isn't always applied and 2 you just don't get enough to make it something to be super happy about.
(This is not the case during jungling as 5 health matters in the jungle, but i am not a bushmaster so i am not commenting on jungling)
Q:
In both forms is based off of the other champions max health, the base damage scales OK. This is still better to level than the E which only reduces cooldown on level up
E:
Human form stun, Spider form Chase and Mini-Zhonya's. NEVER use this skill (in spider form) to initiate a fight, the cooldown is too long to waste it on that when you could use it to mitigate some damage and/or catch up to someone to kill them.

Combo
(Human Form) Q->W->E->R(to spider)->W->Q->E(if needed)->(Wait for Q cooldown)->Q->R(to human)->Q->W->E
Hopefully they are dead... or someone from your team is there.
Also while in Spider form always be autoattacking what you want to kill, the spiderlings focus what you attack and you would be wasting the passive magic damage if you didn't

As stressed throughout the guide you need Magic Pen,



Every Game is situational:
if they aren't building MR then your Magic pen will lose its effectiveness, which will make Abyssal Scepter a good replacement for void staff (provided you are close enough during human form for it to work)
Also if you have a team that is heavier AP than AD you can drop Zhonya's and add grab a Wits End, Banshee's Veil, or Force of Nature

If you want to opt for more damage at the end Nashor's tooth will keep you over that 500 AP mark (I think with rabadons scaling I may be wrong )

Guardians Angle is also a viable option