FARMING
At the start it might be hard to farm in her human form but thats safest way to do it. Q in spider form to finish off minions quickly.
Laining
Auto Q auto to harass enemies with your scorch rune and stuff. And sometimes jump onto them with spider form. A lot of people don't know how strong elise is early game and underestimate her.
When recalling i suggest being in human form so you can E when someone jumps onto you. Without mana go to spider form to E so you can escape easy.
Mid game
Roam, help to do objectives and ward vision is important.

Elise mid is very good but some people might take it as troll and ban elise for you or be toxic sadly thats how league community is. This guide is not serious i made it for fun. Enjoy.

P
In human form her every ability that hit enemy grants her a spiderling in spider form up to 2/3/4/5 based on R level.

In spider form she summons her spiderlings that deal low amounts of damage. Elise gains more % more attack power depending on R level and heal for small portion.

Q
Elise Q in human form deals dmg +% current health with magic dmg. Every level it gives +30 base dmg and cost increases by 5. It's useful to harras but beware of your mana cost.

Elise Q in spider form is short range leap that deals +% health missing magic damage it also applies all on-hit effects like lich bane. Every level it gives +35 base dmg and doesn't cost mana. W in human form can be combined with it making explosive spider jump with you onto enemy.

W
In her human form Elise summons an untargatable explosive spider that can follow nearby enemies and after hitting them or 3 seconds they explode dealing 60/105/150/195/240 +95% ability power to nearby enemies.

Passivly Elise in her spider form grants her spiderlings 5/10/15/20/25% attack speed.
Active Grants her and he spiderlings 60/70/80/90% attack speed for 3 seconds and cancels attack animation on use.

E
In human form she throws a cocoon at enemy stunning them for 1.6/1.7/1.8/1.9/2 seconds and reveals them.

In spider form you leap into the air and vanish for 2 seconds gaining sight in the area of effect. You can recast E to leap onto enemy faster. If you leap onto enemy your Passive effects are boosted depending on level of E from 40 - 100%

R
In human form she transforms into a Spider gaining 25 movement speed and 4 new abilities at the cost of attack range.

In spider form she transforms into a Human losing 25 movement speed and higher attack ranger with 4 new abilities.

How to kill
The combo is pretty easy. You start in human form and do Q-E-W (some say E-Q-W is faster) and then you transform into spider for following with Q and W if target flashes or dashes away use your E to catch him and gain more attack damage.