Think about how grass seed gets sown in nature - it lands on the surface, and then through natural action of animals walking over it, or freeze/thaw cycles disrupting the soil, or wind and rain, etc., it gets lightly covered and some percentage of it succeeds in germinating. Probably that percentage that was most securely covered, but not too deep.
Your instructions are trying to mimic that and maximize the percentage of grass seed that successfully germinates, but the idea of drilling a bunch of tiny little 1/4" holes sounds exceedingly picky to me. And frankly, quite unrealistic.
There's really only one way I can visualize it being done. I have a little device that was passed along to me from my mother that is a bunch of spiky little wheels set on the end of a long wooden pole. And each of those spikes is - you guessed it - about 1/4" long!
It is specifically designed to help sowing grass. The idea is that you broadcast the grass seed over prepared ground, then run this spiky wheeled thing back and forth over it to lightly bury the seed, and then walk it in. And it's very useful for that. But the thing is, other than this one my mother gave to me, I've never seen an implement like this for sale in any garden store. So obviously, people are getting along fine with starting grass seed by just broadcasting it and walking it in. There are also porous mats of various kinds you can buy to lay over the broadcast seed to help improve its chance of germination and to help protect it from birds, but again - lots of people get by just fine without.
And by the way, I don't think "trampling" is really necessary, either. Just walk over the ground back and forth to firm down the soil/compost enough to help keep it from blowing away. Just walking - no trampling.
Okay - after I wrote all that, just for the heck of it, I did some Googling and actually found something like the spiky wheeled little thing I got from my mother. But seriously, I've never actually seen one of these for sale in a store: