Clear the surface, don't worry about any digging at this stage, using shears, secateurs and if you have one a strimmer, these can be hired quite cheeply and really do cut out a lot of work.
Dig out Roots. You need to dig to a depth of 4 to 5 inches, this adds air to the soil as well as removing most of the old roots. You do not need to get every little bit of root. While you are doing this pay attention to the levels of the site, if you have high ares use the excess soil to level out lower areas.
Rake and Tread the Site. You now need to rake the site 4 times, once from each direction. This will give you a reasonable level on which to lay your turf. Once raked go over the whole site walking a bit like Charlie Chaplin, heavy on your heals and close steps to firm the site.
I have chosen to use a ton of topsoil as well for this site. Rake it out starting at the highest point to get a really level surface.
Lay Your Turf. Lay all around the perimeter first then up and down the longest length of the site. Use a half moon or an old bread knife to cut the last strip into the outer strip. Do not tread on newly laid turfs use scaffold boards to move over the site.
Water until 2 to 3 inches of soil below the turf is soaked then for 2 hours everyday unless it has had very heavy rainfall for 2 to 3 weeks. Once the turf has knitted with the soil it is safe to walk on.
Enjoy your new Lawn.