Digging post holes to improve soil

I was hoping to pick your brain for a minute.  I read about your idea
to dig postholes in your lawn and fill with compost to improve the
soil quality.  I am going to attempt this as I think it might be the
easiest way to improve my 'dirt'. I was just wondering how far apart
you would suggest spacing the holes? My 'dirt' is in very bad
condition.  It consists mostly of rocks and dry clumps of dirt.  I
currently have a lawn that is about 75% dandelions and other weeds.  I
was going to attempt the postholes and I thought I would remove all
the sod.  I would then add a layer of compost and topsoil to the whole
lawn and reseed. Any advice would be much appreciated.

How far apart the holes are would depend on the diamer of the holes you are able to make plus how much time and money you are willing to spend.

If the holes were a foot apart, and you had an acre of lawn, this could quickly become too much for you.  Rather, I would suggest that you decide on the amount of holes based on how much you are willing to invest (both time and money) and then try to spread them out evenly.  Maybe try 20 holes.

As for your "plan B" (replace the sod ...)  - if you choose to go this route, leave the sod and get a rototiller.  But I gotta tell ya:  my advice and patience will give you a much better lawn by the end of the year.  After two or three years it will probably look as good as if you had tilled or done your "plan B".  Cheaper and easier.