A NOTE ON BALANCE CHANGES
With the recent balance changes for Greymane, I'm really starting to like the Cocktail build. Infinite long range spammable poke, with some solid burst due to Concentrated Blast. The biggest drawback is the difficulty in ensuring Inner Beast uptime, but it's well worth the trade off in my opinion. The auto attack build is still viable, and one of the friends still swears by it and calls me a scrub who can't land skillshots.

HOW TO PLAY
Scroll down to the bottom to see my full advice on how to play Greymane. The only difference between the two builds is that with Cocktail build you want to be spamming Gilnean Cocktail on cooldown to hit enemy heroes. Once you get the level 1, 4 and 7 talents, the explosion will be very long range and very big, so don't be afraid to constantly toss it in to the fog of war. You should be able to get 95% hit rate easily, even into the fog.

RECOMMENDED ALTERNATE TALENTS
Quicksilver Bullets at level 7 if your team lacks tanks or healers to keep you alive. This is the most important alternate talent.
Concentrated Blast at 16 if your team lacks CC and enemy team is all low health targets.
Alpha Killer at 16 if the enemy team has several high health tanks and your team lacks CC.
Tooth and Claw can be taken if you take Alpha Killer, but I still prefer Hunter's Blunderbuss in almost all situations.
1, 4, 10, and 13 are not worth substituting.

TALENTS
1: Wolfheart is 100% required. 16 seconds is way too long.
4: Darkflight is the best option out of a rather poor tier.
7: Wizened Duelist is very strong, but also very risky. Quicksilver Bullets is a very nice substitute if the enemy team is very aggressive. The extra range allows you to play safer and there is no penalty for dying.
10: Go for the Throat is a fantastic ult and blows Marked for the Kill out of the water.
13: On the Prowl is solid. Visceral Attacks might be worth consideration.
16: I really like Executioner and its synergy with Hunter's Blunderbuss. Concentrated Blast and Alpha Killer are considerations if your team lacks CC.
20: Hunter's Blunderbuss is surprisingly great and the Ult upgrades are rather poor. Tooth and Claw is solid, but harder to get use out of than Hunter's Blunderbuss.

ABILITY USE
Your worgen Q should be used on cooldown. It also can serve as a minor escape in a pinch.
Your human Q should be used a lot, keeping in mind it's high mana cost. Use it on cooldown during team fights and intelligently clear waves with it, for example, don't waste it on two minions, and don't waste it if you're very low on mana, such as less than one hundred.

Both of your W are identical. Use it in human form when you're reasonably confident you can get 8-10 auto attacks off. It doesn't do much in worgen form, but you should have it already activated from human form.

Your E as a worgen should be used as a disengage, obviously
Your E as a human is your hardest to use skill. Once you use it, you don't have an escape for 6 seconds. Use it as finisher, primarily. Don't forget to use it to clear waves, as well.

Your Ult is just a follow up to your E. It can be used before your E, and it has a slightly larger range, so it is possible to use it without E first, but you lose a little burst.

PLAYING IN A TEAMFIGHT
Start in human form. Poke hard with your autos and Q, being sure to activate your W as soon as either of the team's frontline engages. Once an enemy is low or isolated, leap to them with a EQR(Q) combo. You can skip any part of the combo depending on how much damage you need, as well as use Q after R, but remember that won't give you an extra use of R.
Play safe, your autos hit very hard. There's no need to force a kill - that might result in you being killed - with your ultimate.

PLAYING WHEN NOT IN A TEAMFIGHT
Your worgen form is some of the best wave clear in the game. You are a competent merc taker, but your lack of self sustain means it is best done with a teammate.
I can't tell you how to play moment by moment, unfortunately. My best advice is to watch your minimap and err on the side of caution.