Viktor's early laning phase is perhaps the largest stumbling block to new players.
Power Transfer can be used to last-hit minions, as it has a short cooldown and a low mana cost.
Take any opportunity to hit your opponent with Power Transfer, although bear in mind its mediocre range may put you in a dangerous position.
Keep in mind that offensive use of Gravity Field in a lane is very limited, as it costs a lot of mana and has a too short range to be used safely in this manner. Try to use it for zone denial and as a defensive measure versus ganks, rather than relying on it to set up combos.
Death Ray can be used to quickly clear waves when returning to base, or preparing to roam and gank another lane.
Death Ray is also a useful long-range poke/harassment tool, although its manacost is fairly high and should thus be used sparingly.
Viktor's lane presence increases significantly when he gets his ultimate Chaos Storm; combined with his other nukes and an Ignite he can easily burst down most other mages.
Viktor players should also put thought into which of their basic nukes (Power Transfer and Death Ray) should be maxed out first, as both are viable but more suited to different situations.
Ranks into Power Transfer will increase damage and make its cooldown trivial, and the mana cost increase is negligible. The shield strength boost is small but welcome. However, its short casting range will force Viktor to take risks during skirmishes. Max out Power Transfer when Viktor's opponents have little to no long-range option, or if you are confident you can skirt battles without dying. Less practiced Viktor players who have trouble landing Death Ray regularly should also take Power Transfer to keep their damage output up.
Points into Death Ray will also increase Viktor's DPS with higher damage and reduced cooldowns. However the main differences are the casting range and AoE; from max range Death Ray can allow Viktor to damage multiple enemies without any chance of retaliation. A well aimed cast (with some ability power boosts) will also clear creep waves with ease. However, the mana cost increase and skillshot requirement are notable downsides to maxing Death Ray.
In higher level play, you will want to max Death Ray for the majority of your games as it is Viktor's wave-clearing ability, allowing you to quickly farm a wave then move out to take map objectives or gank.
Your choice of upgrade for The Hex Core is a major factor as well, since ranks in the Augmented ability will increase the item's effectiveness drastically.
Smart-casting Death Ray is very different from most other abilities, and will take practice to perfect. One method is to place your mouse at the starting point, then "flick" your cursor in the direction you wish the laser to travel.
Try to wait for people to fully commit to a fight or get trapped in your Gravity Field before using Chaos Storm, as it deals deceptively strong damage-over-time if enemies stay near it.
Don't forget Chaos Storm has a silence on cast, which can be just as useful as the damage.
Keep in mind when the enemy notices the Gravity Field, they will most likely run away (or to you depending on the closest exit). Place your Death Ray appropriately.
Gravity Field can be very powerful for escaping melee attackers. By placing Gravity Field in your path, enemies will be either forced to go around or through it, slowing them down either way.
When escaping remember that the shield from Power Transfer is based on the damage it does before reductions, so it would make no difference in shield value if you aim at a minion rather than a pursing champion.
Rylai's Crystal Scepter grants a substantial amount of health alongside AP. More importantly, its slow effects make your Chaos Storm even more potent as enemies will take more damage trying to escape. If you are close-up to the foe, Chaos Storm's increased movement speed and chasing ability can force them to take all of its damage.
Athene's Unholy Grail is a well-rounded option for Viktor; it solves his mana issues (noticeable when Death Ray is maxed), grants a decent chunk of AP and MR, and perhaps most importantly grants valuable cooldown reduction to increase the uptime of his devasting Chaos Storm.
The Augment: GravityAugment: Gravity upgrade allows Viktor to use his spells more frequently thanks to the bonus mana and cooldown reduction. It also increases the cast range of Gravity Field, making it a better defensive tool and a more viable initiation aid.