Just stick the new turf on the top.
Mind you, what do I know about gardening?
It can be done with no problem, you will have to blin the top layer into the existing..
or you could also depending on time of year spray the area first with a glyphosate based weedkiller ( roundup) and just ruffle up the soil with a springbok rake after 10 days or so then lay the turf on top..
I'd do it in the next month or so as turf tends to knit well in wet conditions....too much hassle doing it in summer..
I'd also throw some growmore type fertiliser under the turf (water it after spreading)......
Too much emphasis is placed on how they do it on the telly..
Like I said if ground levels are okay with present ground...on top with it...
Growmore? an ounce per square yard...
If any further help needed, just whatever me...
Edit...as I say below, if not much depth needed to bring levels up, spread some sharp sand ( not builders!!!) or if more depth, some good topsoil which then must be tramped....just shuffle along one way, when area done..a light rake with a springbok rake then repeat the shuffling at 90degrees...do twice each way..this should remove small stones or lumpy soil...a wee spread of said sand to finish...voila! time to turf...use a plank to stand on if necessary.