I can confirm what max and shobob have said. The worst team to lose a type A gets the 1st round pick, then the next worst record gets the 2nd round pick and then the best record gets the 3rd round pick.
The supplemental picks work a little differently. All the type A's are awarded first and the order of pick goes from previous seasons record as well. So if my team loses a type A and I had the best record of all teams to lose a type A I get the last supplemental pick before any other team gets a second supplemental pick. But, if I lose two type A's, regardless of how good they are, I get my 2nd supplemental pick after every other team has had their 1st supplemental pick and every team with a weaker previous record than mine gets their 2nd supplemental pick. Same thing applies if anyone loses 3 or more type A's. Then after all type A picks are given out, all the type B's are ordered in the same way as the type A comp picks. Until draft prep time the order will show up by time of FA signing but once draft prep starts the picks are re-ordered in this fashion.