Greymane's goal in a teamfight with this build is to pick an enemy and delete them without dying. This build allows him to do this against a full team of opponents and escape. Before level 13, you have to play very carefully, you wont have any immediate escape options if you go in on an enemy close to their team, and you'll have to rely on pressure from the rest of your team to take the heat off you. Once you hit 13, On the Prowl should be triggered BEFORE you engage. This will allow you to kill your target nearly immediately, which gives you the option to focus on escape right away.

Approaching a teamfight, your initial goal should be to engage at range with Inner Beast active. Because of Viciousness, you can use your cocktail to renew Inner Beast if you're having trouble landing a basic attack, and with the 4 second duration, this should be manageable in most situations. Once you have a target poked low enough and within a reasonable range of the engagement (you don't want to chase too far away from your teams support hero) you should engage with Darkflight (not Go for the Throat if you can help it) and burst your target down quickly. If you need to use Go for the Throat to secure the kill quickly, try to do so as the killing blow to secure its second usage. You can use the second cast as an additional mobility tool to jump away from enemy melee heroes, or to secure a second kill if a safe target presents itself. Keep Inner Beast up whenever possible to maintain your 30% movement speed boost, and when available, use disengage to escape from any enemy heroes trying to lock you down.

When picking your focus target, its best to evaluate how quickly you can burst them down. With squishy heroes that have no CC, you can dive them with HP as high as 60% and kill them nearly immediately with your massive burst. With tanky heroes or heroes with powerful crowd control abilities, you want to get them lower at a safe distance first, closer to 25%, before going in for the kill.

Tier 1:

The main aspect of this build is Viciousness. This is why it's risk vs reward, if your Inner Beast falls off, you're gonna pay with a very long cooldown. However, this talent allows you (if played well) to maintain inner beast for the entire fight without the need to recast (which sometimes happens with Wolfheart) to combo well with On the Prowl. Wolfheart is by no means a bad talent, but if thats a talent you want to choose, you should look at a different build.

Tier 2:

Thick Skin is very useful for Greymane. The entire fight using this build is working up to your kill(s). Using the typical Greymane style, you poke and weaken your enemies, then you jump in and go for the kill. The last part of this tactic is where the enemy is really going to try to kill you as fast as possible, and while not all heroes are deterred by block charges, against many heroes, this will save your life. If the enemy team does not have many/any heroes who rely on basic attacks (or they have heroes like Illidan who will just burn the two block charges immediately without getting much out of it) I recommend Insatiable instead.

Drought Overflow is not a bad talent, but it's much better when combo'd with other flask talents, which aren't included in this build. Eyes in the Dark is very cool, but it's easily broken if disengaging from combat.

Tier 3:

For this talent tier, both Quicksilver Bullets or Incendiary Elixer are good choices because they increase your ability to poke from range, which will allow you to maintain On the Prowl easier. Since this is one of the builds main focus they compliment it well. I find Quicksilver Bullets to be more reliable since it doesn't rely on mana (which can be difficult to maintain if you didn't take Insatiable), but incendiary Elixer gives you stronger poke, so either is a viable choice for this build. Wizened Duelist is interesting, but it makes it more difficult to maintain On the Prowl, which often gets you killed, defeating the entire purpose of this talent.

Heroic Tier:

Go for the Throat is crucial for this build. It allows you to catch up to a fleeing target, burst them down quickly, and if you can secure the killing blow, it provides you with more mobility and damage through its follow up to escape, or secure additional kills. Often after diving a target, you end up behind the enemy team and its fun to note that you can use your second cast of Go for the Throat to jump back to the enemy teams frontline, putting you closer to your team, and to safety. This isn't always the best choice however, sometimes its better to use On the Prowl to run out the back instead of jumping on their Muradin and eating a stun.

Marked for the Kill can be good on coordinated teams, but it lacks the fast damage and mobility that Go for the Throat provides against your personal target. Typically, it's not a viable choice for this build.

Tier 5:

On the Prowl is the second talent that is key to this build. A persistant 30% movement speed buff during a teamfight is huge for any character, and with all of Greymanes conditional close/escape, this talent not only helps you secure a kill on your target, but it also supports your disengagement from the targets allies (if necessary). Other talents at this tier can be potent, but if you prefer them you probably should find a different build that focus's on different aspects of the hero.

Tier 6:

This is one of the more optional talent tiers for this build. I find myself often going with Alpha Killer by default, even against targets with lower hitpoints, your fast attack speed during Inner Beast adds a lot of valuable damage to your focus target allowing you to bring them down and get out faster. Depending on your teams strategy, almost any talent at this tier can be viable.

Storm Tier:

The best two talent options here are Tooth and Claw or Unleashed, as they contribute during that crucial moment when you dive into the enemy team for the kill. Hunter's Blunderbuss is a viable choice too since it will help you poke their back line more easily to prepare. Tooth and Claw is the most directly impacting ability, since if encourages enemies to spread out, something you want as Greymane. If not, you can deal massive damage to other heroes trying to support your main target. Unleashed can also be good, the extra use of Go for the Kill is very powerful, but it can be hard to make this happen if the enemy team isn't fleeing the moment you engage, making Tooth and Claw a safer pick.