Power Transfer is going to be your bread and butter in the mid-game. With all the CDR you're stacking the cooldown will be less than 3 seconds. You will basically be spamming this everytime it's up while fitting your other abilities in between. It does a ton of damage and with the Augment: Power speed boost and Death Ray + Rylai's Crystal Scepter you get some serious chasing power.
Early game, you can use this ability to heavily harass your opponent while taking minimal damage. Exchange blows but then stick around for a few auto attacks and whittle them down very quickly while they beat on your shield.
Mid-Late game this will become your primary source of dps. You won't have the added range on your Gravity Field, but with the increased movement speed you will be in a position where you can position yourself better before and during teamfights so that shouldn't be too much of an issue. Try to abuse your mobility and force engagements when your W will be most effective.
If the game is passive, or you snag a few kills early and you manage to get your augment while there is still some laning going on, you can use the new found speed boost to really zone your opposing lane. Stand behind their creep wave and keep them hugging, your shield + boost + snare are more than enough to let you escape if things get hot.
Gravity Field has a ton of uses, and it can single handedly turn the tide of a team fight.
Escaping: To escape a gank, pop it in front of Viktor and walk through its full diameter. Anyone chasing will have no choice but to abandon or get stuned. With your dps combo and tankiness, you can get more than a few kills from gankers who overextend themselves or underestimate your sustain. Occasionally, when facing champs such as Kassadin or Warwick who have built-in blinks that can bypass your escape field, it's a good idea to stand in it and power transfer. They'll get stunned and you'll have a shield. It's risky, but you might have better odds of surviving the gank.
Ganking: Drop it in the opposing champs escape path and go nuts. It also works insanely well in tandem with abilities like Blitzcrank's Rocket Grab, Rammus' Puncturing Taunt as well as the many slows available from other champs.
Team Fights: This is where the ability really shines. Lockdown the middle of a teamfight and pop your ult. Pop it in escape paths. Block initiators from initiating when they want (good for dragon\baron). Cut teams in half. A good Viktor can win a game with a few properly placed gravity fields. It's important to abuse your mobility and sustain to get this placed where it needs to be.
Death Ray is what you will mainly use during the laning phase. It's fantastic for poking, and it deals a ton of damage. It remains powerful late-game as you make your switch to a more tanky and mobile Viktor, but your early game abuse of this ability will mislead most people. You will be a lot harder to kill than they expect.
One particularly awesome characteristic of this ability is that casting it doesn't interrupt movement. It does so much damage and once you throw Rylai's Crystal Scepter into the mix, it becomes an amazing chaser. It's a skillshot, so naturally you can send it through forests and whatnot to catch someone fleeing. I also use it to kill the big ghoul camp from mid when I need some extra farm.
Chaos Storm is pretty straightforward as an ultimate. The one thing I have to stress about this spell is DON'T pop it at the beginning of a teamfight, no matter how tempting that may be. Wait till you land a good snare, save it for when you need the silence, or save it for the 2-3 stragglers trying to escape at low health. It moves faster the closer it is to Viktor, so with your Q spam and speed burst, you can send this thing really far and pick up a lot of kills.
When fighting a champion 1v1 try to use all of your abilities on them except stun and ultimate. Pretend to flee as if you cannot handle the fight and as they are chasing you lay down your stun and ultimate in quick succession. Your other abilities should be off of cooldown by this time so feel free to use those during this time as well.
While laning middle repeatedly poke your enemy with the laser and power transfer until they are about half health. Then when all of you're abilities are off of cooldown stun and nuke.
Try to repeat this strategy as much as possible.
After you have your Augment: Death you should be able to farm an entire wave of minions with one well placed laser. Never use you're ultimate to farm minions unless you are in danger of loosing a turret,inhibitor,etc.