A new lawn, a new dawn
The best time to lay turves is at the end of the month, through October and into November. If you are seeding now is the time to do it, with the ground prepared. Grass seed can be sown by hand and spread in criss-cross fashion for even coverage, spreading half the seed in one direction and the other half at 90º to this. The surface should then be lightly raked into the seed bed, rolled with a roller or lawn mower with roller (without the blades engaged!).
To be more accurate you can set out areas of one metre square and the seed divided accordingly to be evenly spread. Alternatively, you can apply the seed using a seed/fertiliser spreader, which you will need to calibrate and calculate the output over a given area.
Existing lawns will benefit now from scarification to lift out dead grass, moss and thatch, using a scarifier attachment on the garden tractor or a walk-behind scarifier. Cut the lawn quite short to begin with and work the scarifier first in one direction and then across the first pass. Collect the debris afterwards with the collector on the tractor or grass box on the mower. Spiking now to aerate the lawn will also be beneficial for drainage and to help get oxygen to the grass roots.