I would post a screen with my first few games with Elise, but I'm under level 30 so I'll get flamed cause I don't matter.
Elise is a BLAST so play with. She has probably the strongest early game of any champion I've used, which is really due to the fact that her cooldowns don't transfer over to spider form AND her spider abilities don't cost mana (which is insane). At around level 3-4 when you have all your abilities, all you have to do is let your opponent extend just a LITTLE bit to where you can land E. After that, the combo of, starting in human form, E>Q>W>Spider Form>Q>W>Auto Attack is more than enough to kill pretty much anyone laning in mid with you (which is where you should generally be laning with Elise. She's also very good in jungle!) Frankly, even at level 1 you are incredibly dangerous, because you can Human Q, R, and Spider Q to bring opponents down a LOT.
Her ganks are just vicious, and it's terrifying for your opponents :P Hide in the brush near top lane and descend upon an opponent with your Spider Form E and just destroy them with the crazy AS steroid from your W and killing is easy. The versatility you can have by chasing with the gap closers and speed from Spider Form and the ranged mage abilities of human form is crazy. With her amazing early game and ganking abilities I have had AT LEAST 3 kills by the 10 minute mark in every game I have played with her so far.
Her late game isn't quite as strong, and you have to rely on your team to try and separate enemy champions where her monstrous sustained damage can rip opponents apart. While I usually solo mid with her, I did play a game where I went top with Blitzcrank and if he ever landed a grab...the opponent was dead through the crazy damage over time Elise is capable of (plus they have absolutely no chance to escape...Rappel is an incredible gap closer.)
I have NO IDEA whatsoever how to make optimal builds, but usually the core items I've been shooting for are RoA>Rylai's>Frozen Heart, in that order. I'll also have my situational boots obviously and I'll usually top off my build with Rabadon's and Lich Bane or Nashor's Tooth. I think Nashor's Tooth is really good with her, pairing amazingly with her Spider Form W and giving her ABSOLUTELY RIDICULOUS attack speed when she uses that ability. The fact that her W gives her some life steal allows her to heal extremely well with the insane attack speed from Nashor's Tooth. The CDR also helps so you can use all your abilities in Human Form, switch to Spider Form and use your abilities there, and then able to switch back to Human Form and all your abilities will be ready again and you can just keep doing that.
All in all, she's probably the funnest champion I've used and I've been having really good games with her. I do not regret spending 10 bucks so I could get both her and Varus :P