I know it's an old-fashioned idea but I would skim off the turf and stack it upside down and let it break down naturally. I would then loosen the soil to create good drainage before filling in with the new soil. I wouldn't dig in any rotted manure or compost unless you know where you will be planting carrots and parsnips which will be forked if they come into contact with it.

Another approach which I use is to take the turf off fairly deeply (about a spades depth) and bury it where it is upside down. If you have a reasonable depth of soil in your raised bed it is unlikely that any grass will grow through, and you will have a good depth of friable soil when you've finished. I make new beds this way as it avoids carting the turf away to stack and then carting it back when its rotted. I think perhaps it depends how old you are -I go for the less effort way these days! If you have lots of energy Jimmy's method is the classic one.

I like Jimmy's approach. That's what I do. Overturn the old sod, let it break down and add valuable nitrogen & nutrients into the soil. I'd wait until Spring to work in top soil/compost. Consider planting a cover crop over winter to prevent erosion or just let the weeds grow until you are ready to plant in the Spring.