H/T to the Bayly Brothers.
USA Today links the USADA report, and more details can be found from the USADA.
Now a layman's explanation. The main drugs taken appear to be EPO, which enhances red blood cell formation, blood doping (re-infusion of one's own red blood) to achieve a higher hematocrit, cortisone and testosterone. The steroids are helpful in building and repairing muscle.
I'll illustrate the significance with a personal story. In college, I walked on to the track team as a distance runner, and found after a spring of 70-90 miles per week, accompanied by a generally unappealing variety of iron-rich foods at the dorm cafeteria, the local Red Cross blood center refused me. Why? My hematocrit was too low to give blood--below 40, if I remember correctly. The nurse informed me that the combination of endurance sport and low iron diets was linked to this. This corrected, my hematocrit returned to a "high normal" range of 45-47, and I started running faster, too.
Now look at the report; Armstrong, with a far rougher training regimen than mine, was concerned when his hematocrit got down to 41. The cycling federation limits cyclists to a hematocrit of 50--just like the FDA for blood donors, for what it's worth. So what's going on with EPO is that the athlete gets the chance to train much harder, followed by higher capacity to transfer oxygen to the muscles during competition--translating to a 10-20% advantage, or more, in terms of the energy that an athlete can expend without "going anaerobic", which is a 5-8% advantage in peak speed. Blood doping will do much the same thing, except without helping the athlete in training as much--the body only makes so many red blood cells, after all.
Now there are of course limits to what can be done--the body can only process so much sugar and recover muscles so quickly, so it's not quite as big as that. That said, the data presented indicate that Armstrong did indeed have a fairly significant advantage over non-doping participants. How many there were is uncertain, as the cycling federation notes that 20 of 21 podium participants in the Tour de France since 1999 are implicated in doping. Finding a non-doping cyclist could be like finding a Mr. Olympia participant not taking steroids, or a Miss America participant who doesn't know any plastic surgeons.
So the data do indeed bear out the cycling federation. What's to be done? Again, I have to suggest that cycling needs to police itself if it wants to be taken seriously. I'll be waiting for that announcement.