For lawn planting:
1. Spray the existing weeds/grass with Roundup to kill everything. Wait a week or so and then till it under with a tiller, light disc or something designed for turf prepping.
2. Wait two weeks and repeat the spray on anything that starts growing again.
3. Smooth and losen the top of the soil with a spring harrow or landscape rake.
4. Broadcast the seed as evenly as you can by hand or with whatever spreader you can adopt. Use the coverage rates recommended. Too much grass seed concentration can be just as bad as not enough - the dense initial growth of sprouts will choke themselves out and not last very long.
5. Drag the area with a harrow lightly to mix the seed into the top 1/2" of soil. A landscape rake is probably too course for this.
6. Drive over the area in a pattern with the tractor such that the wheels eventually cover the whole area (assuming hard enough soil or turf tires such that no large ruts or marks are made). This will press the seed into good soil contact and seal the surface slightly preventing the seed from washing out.
7. Water every day. An irrigation system is best. The critical time is when the grass first becomes visible after about two weeks. Its real easy to dry it out at that point.
Quick and dirty method:
Skip steps 1,2,3, 5, and 6. Do only steps 4, 5, and 7. Spread seed on top of whatever is already there (mow short first if you like), rake in, and water.
Really lazy method:
Repeatedly spread grass seed over what is already there. Keep it mowed. Years of doing this will produce a nice lawn.