Augments basically make your abilities better.
Augmenting your Q gives you a temporary move speed buff after using it. (Buy this one after Augmenting your E!)
Augmenting your W makes all trapped enemies be dragged to the center. (Great in teamfights!)
Augmenting your E makes all enemies hit by your E take even more damage. (Get this one first!)
Your ult is automatically Augmented after buying all 3 Augments. (Upon buying all 3 Augments, your ult moves 20% faster, which is handy.)
Max your E first. It's your poke which you'll desperately need to use, especially now with AP midlane being so nerfed.
Your Q becomes more powerful if you buy a
because it adds onto the empowered auto attack given by using it. Personally, I don't buy Lich Bane, but if you want your Q to be -about- as strong as your E, go right ahead and buy one.
Your first Augment you should get is for your E, (which improves the damage), great for early to mid-game.
Max your W last. One of Viktor's downsides is he is kind of vulnerable at early-game due to not having very much mobility. When you have your W available, it will count as your anti-gank protection, so use it wisely. The cooldown is a bitch.
Allow me to explain the blue-purple laser thing. When you use your Q, you gain a shield (it won't block heavy damage of course, but it's nice to have), and your next basic attack within 3.5 seconds will do more damage than normal, hence the term "empowered". Once you have your Q Augmented, (typically you might want to Augment your Q after Augmenting your E) your Q will give you a temporary movement speed buff upon hitting an enemy. This is very useful for running away or chasing down an enemy.
Teamfights is one of Viktor's strong points. Remember that despite having massive damage potential, you're STILL squishy at close range, so don't try to 1v5 like a
would do. For example, if the enemies are crowding up/gathered in 1 area, try to bait them into following you and then IMMEDIATELY pop your W. Then use everything you've got at them. (If you've upgraded your E prior to this point, you can deal good damage to 1+ enemy champs by using it here, as the enemies are neatly put into 1 pile by your W if you've Augmented it as well.)
Lastly, don't spam buy Hex Cores when you have the Gold, that method isn't effective anymore. What I like to do is upgrade my Hex Core every time I level my ult. (Basically, upgrade your Hex Core when you hit level 6, again when you hit level 11, and one more time when you hit level 16, IF you have the gold to spare. If you cannot spare the gold, then wait 1-2 more levels and upgrade your Hex Core.)
Hope this helps, and I apologize for the wall of text.