If the dog is with its owner, get their name and contact information (phone number, e-mail, and physical address). You'll also want to record the name of their insurance company, as well as the policy number (for most dog owners, this will be their homeowner's insurance).
Get the dog's info, too (especially if there isn't an owner present). Note the breed, any distinguishing markings, etc. If there are any witnesses, you will want to get their name and contact information as well.
...or admit fault, in any way. Remember, the dog bit you. That shouldn't have happened. You may feel compelled to say "sorry," but keep your injuries in mind. Anything you offer by way of apology could be used against you if you decide to pursue a claim.
Seek Medical Attention
To be honest, this is your main focus. In the case of an extreme injury, this would be your first call, but keep in mind emergency personnel may not pick up on the details of your situation as well as you would like. Also, the more information you can provide about how you sustained your injuries, the better they'll be able to help you. Keep in mind that in some jurisdictions, you are required by law to report any sort of animal bite or attack to Animal Control. Your physician may not do this for you, so double-check to ensure a report is filed (even if you have to do it yourself).
Take Pictures, Talk to Witnesses
Talk to anyone who helped you immediately after the attack. If you decide to proceed with your case, you'll want to have as much documentation as possible.
Determine if You Have a Case.... then SHHH!
You have to determine if it would be worth it to you to bring a lawsuit against the dog owner. Most reputable attorneys will offer you a free initial consultation to discuss your options. Keep in mind that most dog owners are covered under their homeowners' or renters' insurance policies, however you can't always get a copy of the policy without bringing suit.
Until you have made any decisions regarding your case, don't talk to anyone about it other than potential attorneys. This includes insurance adjustors, and anyone else hired by the dog owner!