>Does anyone have any tips they can share about how I should re-queen her?
Yes.
http://www.bushfarms.com/beesfaqs.htm#requeening> I've read so much conflicting information that I'm not sure which way to go. Do I dispatch the old queen, then put the new queen straight in between two frames?
I would not dispatch the old queen until the new queen is settled and laying. Take the frame of brood that you find the old queen on and a frame of honey and put them in another box until things have settled. When you DO get rid of her, drop her in a jar of alcohol and save that for swarm lure. It will get better as you add more queens and they soak longer.
> Should I wait 24 hours before putting her in?
I like overnight. 12 hours is better if it's overnight as they will be quite certain they are queenless and will not have progressed too far on raising a new queen.
>Do I need to put some newspaper around her cage for a day or two?
No.
>Should I spray the cage with some kind of vanilla/peppermint scent first?
I would not.
>I've seen a bloke at my bee-keeping club do it, and he just whacked the cage straight in with the sugar stopper facing up so she wouldn't get trapped.
Exactly.
>I really want to get this right, as if I kill the old queen and the new queen doesn't take I'm thinking I could lose my hive this late in the season.
So don't kill her until things are settled.