Alistar has a couple combos which are all strong. All of them involve Headbutt And Pulverize.

The first is a close range combo, It starts with Pulverize then angle your headbutt to separate The champions and allow for an easy kill.

Second is a long range combo, Start with headbutting them to pulverize before the knock-back takes effect and knocking them airborne instead, then attempt to body-block the enemy while you Carry finishes the kill (Ff you do this aimed at a thick wall it makes it much easier). Note this is difficult to time.

The third is a defensive combo, while your running or under tower and are vulnerable Start a pulverize (so you can aim) then headbutt them over a wall or away to help clear some distance.

Alistar is a very strong support in the sense of having huge amounts of crowd control, good sustain, and is practically unkillable.

Alistar can run as a kill lane beast with all of his crowd control and tankyness.
Or Alistar can run as a passive laner healing his marksman and disengaging from fights that could be life threatening.

Alistar is a well rounded strong champion that can turn around a fight with his ability's in a moments notice. Keep this in mind when you are being ganked, alistar can turn that jungler around and into tower food!

Alistar is great for setting up team fights, many of the tactics involve flashing or headbutting in to pulverize then unbreakable will to absorb the damage while your team follows up and decimates the enemy team!

Alistar excels in the defensive position be sure you make plays with your crowd control.
Try hitting tanks away or hitting weak champions into you team.

Alistar is good for defending his teammates also, when they are in trouble alistar can come in with headbutt quickly then follow up with a pulverize to help allow a easy escape.

Try healing as much as possible in fights to utilize Ardent Censer because 25% attack speed for a whole team is a mind blowing damage buff!

[*] Alistar Has huge crowd control abilities
[*] Alistar has a area of effect heal that works on minion waves.
[*] Alistar ultimate gives him 50-70% damage reduction making him a super tank.
[*] Alistar has the ability to dive tower unhindered and utilscales well into late game.

[*] Alistar can commonly over heal push lanes with triumvirate roar.
[*] Alistar has little range to initiate his combos.
[*] Alistar has little damage scaling with support items, and is practically useless alone.

Alistar is one scary guy to see running up abuse it and make sure to make plays!

And don't forget to protect you team, just like Braum, but Alistar is way better of course.

Good luck, and see you on the rift!