I've got an existing lawn I want to add onto. In the new area, I used to have woodchips, but I've raked them away.

My soil is very heavy clay, with an alkaline ph.

Now I've got these tasks to do, but I don't know the order to do them in:

Dig sprinkler trenches
Run sprinkler pipe
Install 2x4 composite border for lawn
roto-till organic material into the soil

Do I need to roll the soil after rototilling?
How high up the border should I lay the sod? Should the soil be all the way to the top of the border, with the assumption it will settle a bit?

Any information you can provide would be great. I don't want to get in the position of not doing things in the right order, and having it cause me a lot of extra work.

If the picture I'm including works, this is the area I will be installing the new lawn. Current the hose is being used to picture the border.

Ne-ver! Why do you think you need to till it? There are rare exceptions to my thinking. It doesn't look like you have any exceptions from the photo. In fact your grass looks great, but maybe you know something you haven't said. Did some one tell you to till?

Mother Nature applies organic matter every fall by dropping leaves. She applies it all year long from animal dung and urine. She also applies it from plants and animals dieing. Note that none of these methods involves digging up the soil to mix it in. With the exception of underground roots on dieing plants, the application is always done to the surface. You can mimic Mother Nature by applying ground up grains as a fertilizer. The heavier and more frequent the amounts, the faster the increase in organic matter in the soil. A typical application of, say, alfalfa pellets would be 20 pounds per 1,000 square feet. You can apply that 3x per year or you can apply that amount every weekend for a faster effect. Because the fertilizer is a relatively slow decomposing grain (as opposed to fast decomposing animal byproducts), you cannot burn the grass.