The biggest thing you can do is simplify things as much as possible.

Use macros to reduce what you need to hit down to the minimum.

On my druid I am in the process of setting up two macros. One I will hit when I'm building up aggro,
the other I'll hit when I've got plenty of rage - so will add maul in. I may have a third for maxing out single target threat.

On your healer you need to be able to target each player easily.
Have 5 macros - that target different party members and that pops a lesser heal or renew on them. If these are always the same you can put names in - if your 3 dps is made up of random pugs then use party1,2,3,4,5 etc.
You can then press your other healing abilities to top them off, shield them etc. Make sure the keys that target your tank or your priest never change. Have the keys for your AOE heals available.

If the whole team takes aoe damage hit your aoe heal, perhaps a holy nova for a quick heal if they are in danger of dying then your longer cast for a bigger heal.

Other than that a lot depends on the ability of the other 3 players. If it's friends then having them hit the same target, and not over aggroing should make things easier. If you are pugging in the other 3 then you might have to be more forceful in encouraging them to let the tank build aggro, and to use their own abilities to drop aggro.

Oh I forgot - perhaps have a macro that targets either the tanks target if it's friendly or the target of the tanks target if it's not, so on bosses if the tank does lose aggro you instantly heal the player that's now getting beat on. (And it gives you the option of targeting a specific player on the tank to heal, which isn't ideal).

With a good group you'll find that the damage and healing are more predictable. Normally restricted to keeping the tank up and healing the odd player that's damaged - with rarer occassions of hitting aoe healing when AOE splash damage occurs.

EDIT: DAMN - Whilst typing this wall of text three other replies completely removed any need for my post. Sorry about that.