You would be best off removing the old grass as if it was rolls of turf. By using a spade and cutting slices out so that you are lifting the roots and leaving the loose soil below.It can take a bit off hard graft doing this. Once removed you may like to get a few bags of fresh top soil to mix in with the soil,do this by spreading about and raking in then level all the soil,give it a good water so the soil can be damp for when you lay the new turf down. When you lay it down,make sure you lay it like a brick wall effect so there is no joining lines. Water the grass well of an evening when not in full heat of the sun to help prevent burning the new grass. Try not to walk on the new grass for a good month or so as the new roots will be thin and weak as they start growing into the soil below. Let the grass grow well before taking to mower to it. When you do cut it dont cut it realy short for the first few cuts.also start giving it some grass feed to help it on its way. You could put Grass on top of old grass but it could end up a messy uneven waterlogged patchy lawn. Alternative just get some topsoil, lightly spred it over the old lawn and mix in a load of new grass seed, water well, keep the dogs, birds and people off it and let it grow again.Will look a mud patch for a while till the new and old grass comes through.