In addition to the tactics listed by GnomeSlice, the choice of ammo is instrumental in conserving ammo. Especially with Big Daddies. Before I decide to take on one of those, I
- equip the Shotgun with electric ammo
- equip the Tommy gun with armour piercing ammo
- make sure my pistol is set on either regular or anti-personnel ammo (*)
- select the electricity or bee plasmid (I usually prefer the electric in most situations, but that's personal preference)
(*) The pistol is helpful if splicers pop up and want to take part in the action. They can be dispatched most easily and without wasting ammo by paralysing and head-shooting them. You don't have much time when a Big Daddy is charging at you so splicers have to be dealt with quickly.
Now, you can paralyse the Big Daddy repeatedly with either the electricity or bee plasmid or the shotgun. Then hit him with either a burst from your Tommy gun or a grenade (sticky grenades work nicely, too). The armour piercing rounds are insanely more effective than the regular rounds, so you won't waste nearly as much ammo.
Alternatively to the Tommy gun you can also use the pistol's armour piercing rounds. They're incredibly effective, too. But I would always keep one weapon ready to take on splicers.