To quickly knock up an enemy twice W and once it connects Flash to where they will land. Q E before they hit the ground, AA then AA once it's ready.
To extend your engage range W and right as you reach your target Q F instantly.
To knock an enemy back into your team from outside melee range Q and mid animation Flash, then once behind your target use W
To surprise your target with an engage F and instantly W Q one after the other.
To knock an enemy back into your team Q them, then walk behind your target and use W.
Your standard Alistar combo will be to W Q one after another then E once in range. AA then AA once it's up for the stun.
For a longer cc chain using a wall Q and instantly E AA. W your opponent into the wall and stun them with your AA.
To make use of walls on the map W someone into one then AA Q as fast as you can.