In this build, Alistar's role is to become the most untouchable tank / support for your team, with the ability to score a couple kills, and when played to the utmost perfection, never dies.
Definitely suggested for those who are just getting started as Alistar so that you're not just gonna feed off a character you don't know - but also recommended for advanced gameplay as well.

The build is basic, simple, and easy to get the hang of!

Summoner Spells: Heal + Clarity = Effective Laning

1st Ability (Stun) effectively after you knockback. By mid game, you should be able to land a knockback and run close enough to stun. Good stall for allies to come finish the job!

2nd Ability (Knockback) every now and again to toss your opponents back away from getting last hits. An effective way to "deny" them from getting gold. Works wonders against melee characters. Use common sense when doing this. Also effective if they get too close to a tower. Try and aim this ability towards enemies and pin them against walls. Give em the horns!

3rd Ability (Heal) - SPAM THIS LATE GAME - Your cooldown reduction will give you the ability to cast it twice every 10-15 seconds. Effectively, your cooldown reduction will also give you the ability to use a stun or knockback twice.

4th Ability (Buff) - Use this when you jump into team fights, and bash the living **** out of everything in sight! Also good for chase-downs!

Stay safe early on. This requires a cautious mind when starting, but it's a straight shot from finishing your Berserker's Greaves. After that, roam around and bust out those kills to get the upper hand in game. With the right playability, Alistar is UNTOUCHABLE, and you can finish games with anywhere from a decent 5/0 to sometimes a whopping 10+/0 KILL/DEATH ratio!

Start off with building a Shurelya's. This will get fundamental stuff out of the way such as health regen, cooldown reduction, and bonus gold. Stay in lane until you can farm up roughly 2K to finish the Shurelya's. The item also has a movement speed buff, and will take care of your speed enhancement problem until you can farm the next 300 gold for boots.

From here, get another rough 600 gold and finish off Berserker's Greaves. What this does is now you have the ability to initiate team fights, using your 2nd Ability and 1st ability to push in and get the stun off. In addition, you will be able to immediately start swinging, and stacked with your 4th Ability, you will be heavy hitting and give everyone a reason to stay away from you early on. Remember to throw down 3rd Ability heals now and again to maintain optimum survivability in team fights. Use Clarity when necessary to get mana back.

By now, you should be working towards SHEEN. Sheen is a great way to give yourself just that extra punch after initiation. Also helps for last hitting for when you're farming a safe lane. After SHEEN, go for FROZEN HEART for ARMOR + Cooldown Reduction. You should be running in and out of Teamfights just enough to do what you need to do to help your team, get assists, and possible kills, and build that farm up. Your team will love you.

Build WARMOG and FROZEN MALLET. Lots of HP, REGEN, and you're getting just a little more punch out of you with slowing capability. By now, the rest of your team should have everything they need to finish the job, and the most you'll be doing is throwing down your heals and making sure you are pushing lanes with them and wrecking team fights.