Legal eagles, how does it usually go when somebody’s dog attacks you—as far as suing the owner?

[byeya]

4. It goes by local ordance in most states. Where I live there's a leash law. If a dog is unleashed

the animal control officer grabs it and takes it to the pound, notifies the owner who has to pay a fine to get the dog back.
Also here, if you are bitten by a dog, you call the ACO and he takes the dog to quarantine and cites the owner. All costs are borne by the owner of the biting dog. When the owner pays his fine, or is found guilty if he demands a trial, that's when you sue. You will win your case for damages and "pain and suffering" if the judge and/or jury buys it.
Wait for the criminal part to be over before you sue. In most places you have 2 years from the incident; other places, 1 year.