About how deep down is the remaining stump? Do you have it leveled over top now? And has the soil slumped down where the stump was?

The problem is there might still be wood in the soil. In order for wood to decompose the fungi that do the job need air for a nitrogen supply. If they cannot get N from the air they take it from the soil. You end up with a yellow circle where the stump was. It might be that way for 10-20 years until all the wood is decomposed.

Armed with that information you can either dig out the soil over the stump and try to rot it away (takes about 2 years), or you can try it with the grass and see if you get a yellow spot. You can always dig it out in the future if you need to.

If you want to seed it, then you sprinkle some grass seed over the soil and water it. It isn't much harder than that. After you sprinkle, walk on the seed to press it into the soil. Then water lightly 3x per day for the next several weeks until you get about 80% germination. Then start backing off on watering slowly until you are watering once per week in the middle of summer.

This is crabgrass seed germinating season, so don't be surprised if this area is completely crabgrass by late July. But don't fret. It is much better to seed northern grasses in the fall anyway. Crabgrass has finished germinating and you have all fall, winter, and spring to develop a root system that can withstand the summer heat.