All you need is a high quality stereo tape or digital file. On one channel you have a "click track", which is a metronome, usually a high frequency sound that'll cut through on headphones like a cowbell, going DA da da da DA da da da etc. On the other channel you have the vocal. At the beginning of the song, you have an extra eight clicks (two bars x4), so the drummer hears DA da da da (first bar) in his headphones, to get the tempo, then over the second bar, counts in the band by clicking his sticks together (onetwothreefour!) and off you go. On the other channel is the stuff you want routed through the main sound system, ie extra keyboards, percussion, samples, and in Ashlee Simpson's case, the lead vocal, which is obviously in time with the click and in the right places. If you lose the click in the drummer's headphones, or the drummer doesn't count everyone in
OK, or the drummer drifts out of time with the click, or you don't know the song structure, you're fucked. The drummer stays with the click, the band stay with the drummer, everything's great.
The only problem is you can't change the structure of the song. If you jam an extra four bars in the middle of the song, you'll still be playing the last verse when the chorus starts on the backing track. It can make you wish you were in the Grateful Dead and play it differently every night, but the upside is being able to reproduce the record perfectly, and sound really really ace. And have in-tune vocals, in Ashlee Simpson's case.
I'm a professional musician and most gigs I've ever done (x1000s) are with click tracks, and I've never had a problem. I hasten to add that the bands I've been in have used click tracks not cos the singer couldn't sing live, but to have the samples etc. Btw many bands, even rock bands, use backing tracks with a click, to give them the extra parts to toughen up the sound like extra backing vocals or the gospel choir they had on the record and couldn't afford to take on the road. Also, if you have the gear for backing tracks, it's easy to whack on a couple of minutes of spooky bass notes / classical overture etc at the beginning of the show, to come onstage to. All good fun. Hope that helps.
But then again, why all the fuss about her only? Everyone who goes to such a show does lipsync. Compare a singer who's on SNL with the same singer performing in a concert. At a show such as SNL, they sing it exactly like in their single, while at the concert, there can be no lipsync and it sounds more real and authentic compared to the edited single version.