The basic choice you have is to do this on the installment plan over
many years or do the fast solution. The many years approach is top
dressing with a variety of materials as suggested. The do it now
approach is to use a roto tiller to till up what's there and mix in
some good humus to quickly establish 8 inchs of decent topsoil. Which
is right depends on what the long looks like now, how bad it gets in
summer, if the existing grass is a good variety or should be replaced,
etc.

All kinds of material can be used to topdress or mix in, from peat
moss, to compost made from leaves. It depends on what is available in
your area and cost effective.