I have had the same problem with Norway rats. After unsuccessfully dealing with exterminators and the various potions that the feed store sold me, I went online.
I found the best advice at Mississippi State Extension. Here is the short form of what I did. It wasn't quick, but it did the job and we are rat free for over 2 years now.
First thing to remember, though is you are dealing with poison. It can kill your kids/dog/chickens/cat if they eat it. Some of the ones recommended will kill a dog/hawk/cat if they eat a rat that has eaten the poison. Keep this in mind and treat it with respect and caution. I found a cage at a yard sale that bar spacings to keep the cats/dog etc out but let the rats in. That is what I used to put the poison in. I also did twice daily patrols of my yard to pick up dead rats (I killed over 150 over my 6 month campain, and those were just the ones I found)
The most valuable piece of advice I got was to prebait. Where ever you are going to put the poison, start by putting just plain chicken feed. Do this for 2-3 weeks. NO poison. Rats test all new food sources by sending the weak ones in to eat. If they die, the others don't follow, so if you just start poisoning you will get a few, but not many. After 2-3 weeks I was going through about 25# of chicken food A NIGHT, which told me everyone was eating (and I had a crapload of rats)
Then I added a quick kill poison to the prebait, I used Quintox, but you could also use rampage. This poison is a eat once kill that night kind of poison. It is so fast the rats literally don't know what hit them. Use it for a week or until you stop noticing dead rats everywhere.
Next go back to prebaiting for a couple of weeks, the add poison to the prebait. This time used a warfarin type like Tomcat or Jaguar. This kills anyone that was resistant to the first poison or just didn't eat it because they didn't like the taste/smell whatever.
Now you have probably killed most of them and you can begin using bait blocks like Hawk and traps to clean up the stragglers or the new ones that pop in from the neighbors.
The complete directions are at the MS state website somewhere, what I wrote is what I did and it worked for me. It might not work for you. Just remember follow all the cautions on the labels, you don't want to poison "non target species".
Good Luck!