Ladies and Gentlemen, I stand before you today to tell you that the state of my yard is strong. I have finished my initial assault on the dandelions. I am not, for the time being, worrying about the area behind the garage or the easement between the street and the sidewalk. But everywhere else has had a pretty thorough initial pass. From here out I only need to pick any yellow flower I happen to see pop up, so they don't put out seeds.
I did decide to compost what I've pulled. I think I had three different people say I should try it, so we'll see what happens with that. I have a pretty good pile started (see the pic at the end).
I also managed to get the oil changed on the lawn mower and mowed the lawn. I cut it fairly close the ground, and then raked up the clippings and added them to the compost pile. There was quite a lot to rake. With the lawn cut and raked I spread out six pounds of grass seed. I concentrated on bare patches left from pulling dandelions and other activities, but I also did some general over-seeding as well. It's supposed to rain tonight and most of the day tomorrow, so I haven't watered the seed yet.
Now I need to think about how to proceed going forward. I really don't know anything about this, so any suggestions are appreciated. My current plan is to wait at least three weeks before mowing again, unless I hear some better advice. The risk there is that the creeping charlie, which the yard has in abundance, will get very large again, but I want to wait so the grass seed can take hold. Then I'll mow with the deck on the mower set as high as possible, and continue that for a couple weeks before putting it back to the normal position. I'll also continue to go out each evening and pull any dandelions I see that have flowered, and for the next couple weeks I'll also use the hose to water the seeds if it hasn't rained that day.
Here's a picture of the compost pile. I'm disappointed in how my cell phone focused, and the picture makes it look much smaller than it really is.

The new compost pile.