The first thing you need to do is find out if any grass will grow in
your area with that amount of sun.

I dont think there is a need to add amendments to areas to be sodded
other than starter fertilizer if the soil is poor.

I spray roundup to existing turf if there is much of it, if its mostly
bare, I skip this part. After it dies, I scalp it with a mower, then
till it up, remove debris, and level it. Then lay your sod and water
it like the previous poster advised. Make sure you stagger the joints
like bricks, and lay perpendicular to the slope. I use a hatchet to
cut it. Not much to it really. I dont use a sod cutter because I
dont find it necessary, dont like removing any topsoil, and the sod
will smother weed seeds.

Adding compost type amendments may not hurt much, but unlike planting
beds, I really think it is a waste of time and money on lawn areas. I
have done a lot of it both ways and I have never seen a difference in
the establishment of the sod. In fact if too much is added it fluffs
up the soil too much. I do add topsoil if the existing topsoil is too
shallow.

The most important things in establishing new sod is putting it in
proper light, laying down fresh sod, and watering it once down. Sod
that has sat stacked on a pallet too long heats up too much in the
middle, pretty much cooking it, so make sure it is fresh.
Good luck,
Bryan