You can put down sod in your area just about any day of the year. If the high temp is in the 40s, maybe wait a few days. But the rest of the year you are golden.

We don't cut the pieces of sod unless we need to go around an obstacle. Here's some St Augustine sod I put down last fall. I'm guessing this is 50 pieces of sod.

As for prepping the soil, the information you are getting is very popular, but it is WRONG, in my opinion after reading lawn care forums for 20 years. Possibly the worst thin you can do for a lawn is to rototill. I'm not sure where that information comes from, but it is very popular in newspapers and magazine articles. Some landscapers like to do it because they have a rototiller they need to be making money with. Rototilling sets you up for a lifetime of bumpy soil. It can be fixed, but just don't set yourself up for such a failure. Instead just start with the surface you have. It might be bumpy, but we'll address that. Here's one way to get off to a great start.

Water your future lawn area lightly, 3x per day, every day for a week. Weed seeds love this continual moisture and will germinate into new plants. At the end of the week, spray with RoundUp. Continue watering to pick up any slow germinating weeds. At the end of the second week, spot spray any new green stuff with RU again. That's it for weed control. Now let's look at the surface. If your soil does not have any spots where water pools up after a rain, then you are probably off to a good start. Push your lawn mower around to see how bumpy the surface is. If it rolls like a golf green, you're ready. If the mower bumps around, then now is the time to level the surface. Surfacing is easy in theory, but can be back breaking. The idea is to bring down the high spots and bring up the low spots. If you can scrape off the hills and move that soil into the holes, that is the idea. If you need more soil, I suggest buying it in bags so you can return what you don't use. Sand is nice because it settles immediately. Basically you scatter the sand and use a drag to level it over large areas. You can make a drag with a 2x4, 8 feet long, and some chain link fencing. Attach the fence to the 2x4 and pull it along behind you to level out the sand. Once it seems perfectly level, it's time to water. Watering will settle the sand or soil right away. Then recheck for any water pooling. If you have low spots, add more sand, drag, and water. You should have to do this no more than 3 times to get it perfect. Then when you lay the sod, lay it so you don't have to walk over the newly leveled surface. Always walk on the new grass. I'm assuming you have a typical sized lawn for the area. AFter putting the sod down, you have to walk over every single square foot of the sod to press it down into the surface. Roots will not grow through the air to find the moist soil below. If you have a larger lawn you can use a rented roller to roll the sod down. After the sod is down, start watering. Water lightly 3x per day for 2 weeks. The soil should never be squishy under the grass. If it is, you're watering too long. All it needs is for the underlying soil to be moist - not saturated. After a few weeks the grass should be knit down to the underlying soil. You can start backing off on the frequency and go up on the duration of your watering. St Augustine roots will grow fast enough that you should not have to worry much after a month. Ultimately you will be watering deeply (1 inch all at one time) and infrequently (up to once a week during the hottest heat of summer). In the cooler months of winter, you can water 1 inch but only once a month. New sod comes fertilized. If you get it down now(ish), you can use a starter fertilizer and then get ready to use a regular fertilizer on Memorial Day. You should not have any weeds if you prepped right, but if you see some in April, that is the time to spray them unless you want to pull them.

Call the sod farms on this list to see what varieties they have available. You might be able to buy from the farm or ask where they sell their products. I would not do an entire lawn from Home Depot. Sure they have grass, but it's not very fresh. Sod should be cut and installed the same day if possible. The nursery where I bought mine sells 14 pallets of St Augustine per day, so it's fresh every morning.

It is likely you do not need to add more topsoil. In fact with the maturity of your neighborhood, it is much more likely that you should remove soil to bring it down to the level of the surrounding concrete. If you post some pictures we could help you evaluate the situation, but unless this is a new home and newly graded, I'm betting it has too much soil already. Small amounts of 'too much' are fine(ish). It's a professional job to remove a few tons of topsoil, though.

You can mow the new sod when it gets up to 5 or 6 inches high. Then mow it back to the mower's highest setting. Always check the soil before mowing to see if it is squishy. If you are still watering lightly, the soil might not be dry enough to mow over.

Thank you.