Headbutt is a targeted ability that knocks back one enemy, making it an effective peeling tool.
Alistar's famous Headbutt + Pulverize combo is one reason he's so strong, since he basically has a short-ranged Unstoppable Force on a ~10 second cooldown come late-game. The best way to pull off the combo is to press Q while Alistar is in the middle of his Headbutt dash.
The combo can also be reversed: if you can get in range, Pulverize can stop enemies long enough for Alistar to move behind them and Headbutt them into your team. Flash can help you close the gap.
Headbutt can also be used as a powerful stun, if you manage to knock the enemy into a thick enough wall. The targeted unit will still try to travel the full distance of the knockback but will be stopped by the wall, leaving them airborne for the duration. However, if the wall is too thin you might knock your target through it, allowing them to escape.
Headbutt's dash can also serve as an effective escape tool, as long as there are enemy champions, minions, or monsters around to target.
Trample is a point-blank area-of-effect ability that damages enemies around Alistar and ghosts him. It also allows you to stun a single enemy.
Trample provides Alistar with some extra wave clear, allowing him to push waves if you use it.
Trample also allows Alistar to ignore unit collision, which can be useful in chasing or escaping enemies.
Cast Trample at the beginning of a teamfight to get your stun available quickly. Use it to peel for your carries or lock down an important target, especially when your other basic abilities are on cooldown.
Unbreakable Will is a self-targeted active that removes all hostile crowd-control and gives Alistar significant damage reduction.
Unbreakable Will's damage reduction makes Alistar deceptively tanky, even when he doesn't have many items. This allows him to dive turrets very effectively once he hits level 6.
Remember that Unbreakable Will only removes existing crowd-control effects, not future ones. You should try to bait out crowd-control abilities before you activate Unbreakable Will.
Alistar suffers from high mana costs and long cooldowns. Mitigate this by building items that provide mana and/or cooldown reduction, such as Frozen Heart or Redemption.
Even though Unbreakable Will provides Alistar with a lot of tankiness, it has a short duration and a long cooldown, and enemies that deal true damage can still burst him down relatively quickly. Building items that provide health and resistances (Warmog's Armor, Randuin's Omen, Banshee's Veil) help make Alistar even tankier.