Visage is all about blowing people up with his superior DPS. The best way to play him is as a roamer/ganker. Build him as a Semi-Carry if you want to see him really show off. But if there's already a semi-carry, support role is a viable option.

Start off in lane by trying to get first blood. Alert your lane partner and then Grave Chill any enemy hero out of position. Starting off as a trilane can work well with this, as it can guarantee the damage needed to kill. After the first blood attempt, look for another lane to gank. If there is no kill opportunity in any other lane then do your best to stay useful in the lane you stay in! Try harassing down the enemy hero you'd like to hinder. At level 3 you can begin to look for an opportunity to aggressively push the enemy out of lane. If an enemy has 1/2 or even 2/3 of their HP, putting yourself into what appears to be a vulnerable position, and making the enemy turn on you, can mean an easy kill. Soul Assumption is the key to this as it collects charges from damage being dealt in an area around Visage. So long as the enemy has less HP when the fight begins, you should be able to deal more damage than they can. Soul Assumption does approximately 215 at level 1 and 280 at level 2. This is an incredible amount of damage for early game.

If you're going semi-carry, pick up the Ring of Basilius and Phase Boots first and foremost. RoB allows you to cast a bit more freely, and increases your damage and armor. Phase Boots increase your damage even further, and more importantly, allows you to move around the battlefield incredibly quickly. During a gank or teamfight, use Grave Chill and Phase Boots as a tool to quickly outmaneuver the enemy. Plausible situations for this are: quickly moving around a clump of trees to keep vision of an enemy; briefly moving out of vision during a teamfight to reduce attention, only to reappear and use Soul Assumption for massive damage; overtaking a closer enemy to Soul Assumption a low health enemy who has moved farther away. Keep an eye out for these types of situations.

Maelstrom is a strong pick-up for Visage due to his Grave Chill and the improved ability to farm. If you get this item around the 15 minute mark, you can deliver enough damage to quickly kill a support, or help beat down a tank or carry. The DPS should not be underestimated.

Finally, Shadow Blade is amazing on Visage and allows him to deal an insane amount of damage, with little danger to himself; effectively making him an unavoidable threat to the enemy team. Always try and get the attack out of invisibility for the extra damage. Even Shadow Armulet can be useful, as Visage is a hero that, if forgotten, can wreck the back-lines of an enemy formation. If your team has a strong frontal assault, try going invisible in an area that the enemy team will pass. Then push the enemy into a position of retreat, so they pass you by once more. While they are retreating, they are vulnerable, and will tend to panic rather than react aggressive. Grave Chill, Familiars, and Soul Assumption can quickly pick off any target - allowing your team to continue the assault.

Winning a mid-game fight follows the same formula most every time. Grave Chill your target, right-click your Familiars onto the target, Soul Assumption something to death, choose a target for your Familiars to stun, rinse & repeat. It's not rocket science, but it does take focus, and quick fingers.

Tips and Tricks for Visage:

When not using Familiars, just right-click them onto Visage so they follow him around. Treat Familiars as an extension of Visage.
Don't try to be too fancy with the Familiars; just right click them onto an enemy, wait for them to run out of damage, press Q, press Tab, press Q. This lets you focus on using Visage, but squeezes every last drop of use from Familiars.
Try to stay in the middle of the fight, keeping some attention, absorbing some damage, but never killing yourself before you're out of mana. You need to be spamming Soul Assumption the moment it comes off cooldown in order to make yourself as useful as possible.

Friends:

Zeus: gives you charges fast and increases nuke down potential
Undying: this is a hero with a lot of sustainability, extending out battle times, and allowing Visage to spam Soul Assumption for as long as possible.
Shadow Demon: a good addition to most any team. Soul Catcher + Soul Assumption is a frightening combo.
Keeper of the Light: one well placed Illuminate in a team fight can give you max charges.

Enemies:

Gyrocopter: flak cannon can quickly kill your familiars, forcing you to keep them away from the battle initially
Axe: spin kills familiars if they get too close to him

Example replays:
134489103: 11-2-8 best example, against good players, but superior map movement by me
131289366: 30-2-14 pubstomp!!!!
132165312: 29-8-18 pubstomp!!!!