Beastmaster. How do play it?

Beastmaster's primary role is as an initiator with his ultimate, which is notable for its ability to pierce magic immunity, making it a great asset against heroes who rely on Black King Bar (or rage in the case of Lifestealer).
Wild Axes are his main tool in the early game and they are good for both farming and harassment, and their composite damage (both magic and physical) allows them to damage ancients, which allows Beastmaster to do some cool ancient stacking when playing in the dire offlane. Beastmaster is also sometimes played as a solo mid due to his ability to get farm, though he usually needs to utilize Bottle crowing in this position to keep his mana up.

His passive inner beast allows him to amplify his team's damage output in teamfights.

Beastmaster's Boar is like a mini-Viper that slows enemies down if they try to flee and reduces their attack speed if they decide to stay and fight. The eagle is great for its vision and its ability to traverse terrain; late-game teamfights are often won and lost based on which team has the better initiation and reaction, and the eagle's vision allows you to get those key initiations.

Because Beastmaster is a hero that is played primarily for his spells, he doesn't really scale well with items as a carry would. The fact that Beastmaster is able to get farm but lack of scalability means he's frequently a candidate for Mekansm, since he's usually in a position to get gold fast without needing to spend it on items to increase his own attack damage. Beastmaster can also frequently be seen purchasing items to amplify the impact of his spells, most notably Aghanim's Scepter (which enhances the range of his ultimate and also reduces the cooldown), and to a lesser extent Refresher Orb.

Beastmaster's role is Utility (basically somewhere between support and semi-carry).

Laning

He used to be a potent offlaner becuase of Ancient stacking. However, teams figured out that if you push the lane hard, his stacked camp is very easy to steal.

Right now, he's basically just a solo mid (he can still stack Ancients from Radiant mid).

Ancient Stacking

All you need is Soul Ring. Throw Wild Axes at xx:52, or use your Boar to stack for you.

Items

In a competitive game, you'd most likely rush Aghanim's Scepter. This gives you a very spammable ult. However, in pubs, I really think rushing Necronomicon is far better. It gives you a lot more push and team fight when you can't rely on teammates to do what they're supposed to.

Core

• Soul Ring - used for ancient stacking. You can skip it if you're mid and have Bottle
• Power Treads - get Brown Boots and keep them there if you want to go Boots of Travel at some point. Otherwise Treads are a good option because of Tread Switching.
• Phase Boots could also work. You have an attack speed aura so the damage could be nice. It also would help you catch up to a hero after you ult them.

Big Items

• Aghanim's Scepter - the power of the stun, added range, and spammability make Aghanim's Scepter an easy choice to farm up
• Necronomicon - these guys + your Boar + your aura + your stun make easy work of any hero. You can also push incredibly fast given an opening. The Necronomicon Warriors are incredibly powerful, even more so if you micro their spells.
• Blink Dagger - gives you a lot more initiation power

Luxury & Late Game

• Assault Cuirass - the added attack speed and aura help you and your summons push
• Boots of Travel - gives you a huge global presence because you can teleport to your Hawk (or Boar for that matter)

Situational

• Drum of Endurance - benefits your summons, plus gives you some decent stats
• Vladmir's Offering - benefits summons, good utility item for your team & pushing
• Medallion of Courage - use Medallion -> Primal Roar -> wreck them. Duration is similar to your ult's, benefits your creeps, and helps your team Rosh as well.
• Bottle - if you're solo mid

Skills

There are two styles of playing Beastmaster, for the most part.

Summon Heavy

• 4 x Wild Axes
• 3-4 x Summons
• 0-1 x Inner Beast
• Primal Roar

Getting Summons to level 3 makes a huge difference so that you can get the Hawk upgraded. Otherwise the Hawk kind of blows (a.k.a. "bird of feed").

You can use your Boar to stack ancients. He also works well to help zone out heroes, last hit, and secure kills with his slow.

Aura Heavy

• 3 x  Wild Axes
• 0 x Summons
• 2 x Inner Beast
• Primal Roar

This helps naturally push the lane while at mid, giving you an easier time getting runes. Axes help with farming and pushing, but it's not always enough. They also take a lot of mana to cost.

Aura also helps if you're planning to do an early Rosh, do early team fighting, and/or have a carry that benefits from it a lot (e.g. Tiny).

Summon Usage

Boar

• Stacking ancients
• Zoning heroes (especially melee)
• Slowing enemies
• Last hitting

Hawk

• Watching Rune
• Scouting dangerous areas & Rosh pit
• Creep to TP to with Boots of Travel

Axes

This is your primary farming mechanism. Hit creeps so that you can kill them in one axes. This reduces the amount of creeps your enemy can deny. It also sets you up for getting runes.

They deal composite damage, so you can use them on Black King Bar's heroes, Ancients, etc.

The range gives you a lot of harass space. Just be careful targetting them so you hit with both Wild Axes.