So you were going to leave the old turf and then add top soil etc as a blanket-my feeling is in two years time you will be kicking yourself in anger
Organic matter is manure or well rotted garden compost to add structure to the soil-I would prefer to spend money that rather than top soil-you can buy it in bags or a load
So yes remove the old turf -rotovate the soil -add the organic matter-fertilizer- level soil-lay turf.
It is not as simple as that-have a look at youtube for some instructional videos or have a read-up but what I have said is the basic idea
It is a bit like decorating it it all about the preperation and should not be rushed-worth doing properly and only once