Big Daddies spawn in most game types, but I'll focus on Civil war, since it's the only thing anyone plays anymore. Here's a few tips for dealing with them;
1) Turrets; Big Daddies greatest weakness. Without plasmids or regenerating health, and with the larger frame making it harder to hide, they can either ignore it or focus on it entirely. It doesn't matter which they choose, the turret can still easily take out half his health fast. Vending machine traps are less effective, but still helpful.
2) Cover, plasmid, cover. Use your regenerating health to your best advantage. Charge up incinerate, duck out of cover, fire, and return. Incinerate is the only one of the starting plasmids that will work here. This way is very slow, and you're vulnerable to kill-stealers.
3) single-player style; just like in the campaign, use shock and freeze on him, then open up with your best weapon. Note that big daddies already turn slow, so slowing him further with with a plasmid will make strafing even more important. I once saw a player melee a bid daddy to death by shocking him and running around in a circle, but that takes a lot of skill.
If none of these are available to you, it's still worth it to shoot at him. You could get lucky, and even if you hit him once, you'll get credit for an assist. It's also worth mentioning that, although he loses all research bonuses when he upgrades from splicer to Big Daddy, you don't lose yours on him. If you're lucky enough to have a bonus on him, taking him down will be much easier.
You could also boost this. It should be pretty obvious how.
If you have any questions, further advice for this game, or ways to improve this solution, please post a comment.