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I'm going to keep this as small and concise as possible
Alistar can be a great tank/support/pusher character if properly built... unfortunately I see many people building up Alistar in strange ways.
Chances are you won't be needing your Heal at first level... I usually grab the AoE stun if I'll be heading into a lane where first blood is a possibility. This also helps you save an ally if they decide to run off and get beat on.
Above is the general order I follow. I grab Headbutt for some early Pulv + Headbutt setups.
Continue to max out Heal then Pulverize, followed by Headbutt (Always grab your ult when available...)
Here is where you have a few different options...
1. Start off with a Saphire Crystal and 1-2 Potions (Suggested)
2. Start off with a Meki Pendant and 1-2 Potions
3. Start off with a Mana Manipulator '
Option 1 will allow you to upgrade into Tear of the Godess which will take care of Alistar's abysmal mana pool.
Option 2 will allow you to upgrade to Chalice for the extra Magic Resistance. This doesn't solve the "low mana pool" problem, but it will give you quite a bit of staying power.
Option 3 will allow you to rush to your Innervating Locket sooner (Suggested if you have a a mana hungry laning partner)
The general idea of the build is this past the first item...
The games honestly never end up lasting much longer than this. I suggest Mercury Treads do to the fact that... well.. they're ridiculous. Innervating Locket is a no brainer... it makes your heal spell pump everyones HP/Mana constantly. Aegis is a great defensive team item...
Once you've grabbed the basics
(Tear/Mercury/Locket) then its up to you. I *highly* suggest Aura items. Be your teams Aura carrier.
You are a mobile healing unit. Thats pretty much what this comes down to... you are NOT going to be doing tons of damage everywhere. Your job is simply to play the ultimate team support. Stick with your team, heal them, stun the enemies, stun enemies chasing them, stun anything that threatens them. Save your ultimate for when you are taking a beating or leaving the scene of a teamfight (I always try to be the last one out in order to stun those who are chasing us)
I could keep writing about Runes/Masteries... but... they're pretty simple. You are a tank. Drop your points into Defensive/Utility and you'll be fine. As far as Runes? Dodge/CD Reduction/HP all work fine.
Cleanse/Promote/Rally/Fortify are all good choices. Clarity is useless as you should never have mana issues after your first item.
Tear of the Godess
Run around. Spam heals. Stun. Lead charges/create pushes.
You'll never end up doing much damage but if your team has their heads on straight (and stick near to you) then you'll do fine.