Same problem 2 years ago. The ground was rather dry (very dry, Norfolk!) so I had to break up the surface with a harrow first to provide something to cover the seeds or the birds would have had it all.
Then I used canes to mark two opposite sides at 2m intervals to give me some guidelines. Sprinkling the stuff on wasn't a problem walking towards each cane in turn. I figured I could throw the seeds 1m either side of my track fairly consistently.
Then I went over the land with a chain harrow smooth side down to cover the seeds as much as possible.
The grass came up fairly sparsely at first but by last summer (first full year after planting) it had spread to give a complete covering.
I use the area as a parking space (car, trailer, tractor) and to fit attachments to my tractor before working on the rest of my field so it isn't used with animals or to cut hay. The ground is too poor for that and I don't want to use lots of fertilisers.
So, if you want to have a dense growth quickly you might be best to adopt a more scientific approach. However, given some time and patience, this is an economical approach.