Runes are pretty subjective. You could go for HP quints to reduce squishiness, attack damage quints or marks, it's whatever you prefer really. My preference is armor penetration marks and quints and some defensive seals and glyphs.

Going with full attack speed runes is also an excellent choice for Twitch.

Explanation

I've seen a lot of Twitch builds, but none of them are quite like mine. Most suggest either Infinity Edge first, two Phantom Dancers right off the bat, or really fast lifesteal with a Bloodthirster. Here is the explanation for my sequence:

Doran's Blade makes Twitch a little bit less squishy and gives you minor lane sustain. Some people prefer to go for Brawler's Gloves and Health Potions, but this leaves you incredibly vulnerable to lane harass.

Beserker's Greaves are self-explanatory. Twitch is all about Attack Speed. If you are heavy on ganking/roaming, Boots of Mobility can also be a great option.

The Black Cleaver gives you a bit of everything you need: excellent damage output and ganking potential with attack speed, attack damage, and armor reduction to help you AND your teammates deal extra damage. The only problem with getting the Black Cleaver first is the BF sword's large gold cost, leaving you slightly weak since you cannot build into smaller items first, like with the Phantom Dancer. I think it's completely worth it though.

Phantom Dancer second because it's required on almost every AD carry. There's nothing in the Phantom Dancer that Twitch doesn't make use of.

Infinity Edge for massive damage output. After you get these three core items, you're a force to be reckoned with.

Bloodthirster to stay alive in teamfights longer.

And last but not least, your survivability item. The game will rarely last long enough to get this, but if it does you can get either this, Frozen Mallet, or Warmogs. Any of the three are excellent options.

Explanation

Ambush at level 1 to check bushes and for attack speed in case of an early fight.

Expunge is your most important thing to level up fast, because it will finish off your fleeing enemies.

Debilitating Poison right after your ultimate, then max it last. In most games you will be roaming at level 6, so it helps secure a gank.

Spray and Pray whenever physically possible of course.

Explanation

Summoner Spells are very much about preference. I prefer Surge because it gives a bonus to your most important stat - attack speed, and level 1 fights will favor you highly when you throw on Surge.

Teleport for backdooring.

Alternatives

Ignite
Flash
Cleanse

Anything else isn't worth it on Twitch.