How long to accomplish this?
To be totally honest, I don't know an exact figure. I've never actually had to use this method (all of my kids have thankfully been fairly easy eaters), but I know a bunch of herp keepers who have and still do. It can vary from snake to snake since they're all individuals, but from what I understand, wait untill the snake is very comfortable with the step you're on before moving on to the next.
As for what to do with the live rat, I can think of two ideas off the top of my head:
1) Pretty brutal and I'm sure I couldn't do it myself, but I'm pretty sure you could take the live rat, instigate the feeding response, then quickly remove the rat and humanely kill it either via CO2 chamber if you're fancy, by disconnecting the spinal column, or by providing a swift blow to the head. CO2 is safe because it leaves no harmful chemicals in the body - lethal injections/overdoses/ect. will pass on the toxins to the snake and are therefore EXTREMELY dangerous.
2) See if wherever you get the live rat from will either loan you out a feeder rat or let you buy it and then return it for a refund later.
I should also mention that there are tons of other methods to get picky eaters to eat. Some snakes take f/t once it's been dipped in chicken broth, others can be triggered into a feeding response by "braining" it (opening the skull to expose the brain), the list goes on and on. A great resource is reptileforums.com - it's a lot like this site in that there's a ton of extremely helpful, experienced keepers who are more than happy to answer questions.