Like most people, I wrote this guide because I haven't seen one similar to my play-style and my setup is strong enough to share with others. I haven't been playing League of Legends for an overly long period of time, but have enough experience to give advice to newer players. Minor tweaks to the build may suit the way you play, but the overall use of offense mastery + clarity + a strong farming ethic should be used to have success with this build. The best way to take full advantage of this item setup is to achieve a rabadon's deathcap, archangel's staff, and t2 magic pen boots before the 25 minute mark. This can seem pretty ambitious at times but if you are able to accomplish the build by this point you will be destroying EVERYONE on the other team.

Stick to these runes. You will start with a solid 30 AP (with masteries) at the beginning of the match and should be able to solo kill effectively by the time you have Q farmed up to around 50 total AP. Some people like to go for CDR to throw out more stuns, but just focus on making quality stun drops and you won't need the extra CDR.

For a while I used the typical caster build that picked up magic penetration in offense then maxed out utility. The new changes to offense give a nice boost to your damage and the lack of mana regen by not taking up utility can be countered by careful Q farming and strategic use of clarity.

I like to get tear of the goddess ASAP to increase max mana early game. If you are farming at a decent pace you should have about 1,000 gold by the time you make your first recall and can pickup tier 1 boots with your tear. This has a huge effect on your AP endgame so you want this item first, but it is not crucial to build Archangel immediately. Next focus on your Rabadon: Needlessly large rod provides a good boost to your AP early game and is a more effective purchase early game than Magic Pen items because no one really has magic resist in the early game. You might even build your Rabadon before you buy tier 2 boots depending on how good you play. A good way to gauge yourself is you want to have around 100 AP by the first 10 minutes, and 200 AP by the 20 minute mark. By the time you get to the 25 minute mark you should have completed boots, Rabadon, and Archangel Staff. This should net you about 450 AP. This is a huge jump within 5 minutes and you should really start dominating people on the map. From here you can decide if you want to purchase a second Archangel, or you can start to adapt to your opponents items. Lots of MR? Pickup Void Rod. Lots of HP? Keep stacking AP. Rod of Ages seems like a nice buy but the extra HP will not save you if you get caught in a stun. Veigar is all about poppin in for a combo then backing out. I've sat in teamfight for 15 minutes with 30% hp and not been touched because I commanded so much respect with stun + my 2 hit combo. Just realize if you get to 400+ AP before 20 minutes everyone on the map will be running from your stun, but they will also be focus firing you. It's a double edged sword.

Use your own judgement on skill sequence. I didn't even fill it all the way out because I have never used the exact same sequence. It's always a good idea to have 2 points in baleful and 1 in dark matter and 1 in horizon before you decide to take a third rank of baleful. If you are fighting against a noob who can't get out of stun fast enough to avoid dark matter then take a 3rd rank in baleful strike. If they're getting out of range quick enough take a second rank of horizon to lock them in longer. You should definitely take a second rank of dark matter before you take 5 ranks of baleful, because it helps keep farm up. If you have a good team and they take advantage of your stuns, feel free to max it sooner than later, and get some easy assists. If you want to be a gank artist and are confident in your ability to trap other players, max your dark matter with 2 ranks of horizon and you should have some nice 2 hit combos + your ult.

Clarity gets a lot of hate because of it's lack of use endgame but with this build you will take so much advantage of it early game, and may not even make it past the 35 minute mark because the other team will have surrendered likely.

Flash is nice because opponents will stay out of your range when they're ~50% health and know you can baleful strike + ult their face off. flash in front of them and Q + R and start laughing.

Some people like to use ignite but this will lose utility way faster than flash.

To summarize:
AP/Magic Pen/Mana Regen runes to ensure you pack enough punch early game and have some sort of mana regen.

Offensive based masteries to fully take advantage of the massive amount of AP you will achieve late game.

Rabadon's deatchap coupled with 2 Archangel's staves provides huge synergy for mid to late game domination of all AP and anyone not stacking tons of magic resist

Focus on farming your Q exclusively until you reach lvl 6. If you waste your time trying to gank the opposing champion too early you will likely be outmaneuvered and killed (thus slowing down your farm.

Clarity should be used early and often to take full advantage of the mana gained and to compensate for the lack of mana regen from the utility tree.

Flash needs no explanation but, nonetheless, take advantage of its defensive AND offensive capabilities.