Hi! Welcome to the forum. I took the liberty of moving your post to the Lawn Care forum where more people will see it who might be able to give you a good answer.
I think a lot of the answer is prevention. Moss is favored over grass when the conditions are cool, wet, shady, and when the grass is thin. So you want to do what you can to prevent all that. Wet you may not be able to do too much about if you are in one of those parts of the country that had a very rainy season, but you can dethatch and aerate the soil, to make sure it's very well draining. If your lawn is shady, consider limbing up or thinning trees to let more light in. If this is an issue, consider planting a more shade tolerant grass variety. Work to make your grass more vigorous with compost, nitrogen fertilizer, etc. Corn gluten meal is not only a pre-emergence weed suppressor (doesn't work on the moss though), but adds nitrogen to the soil. Now and in spring are good times to use it.
If your soil is acidic, that tends to favor moss as well, consider liming the soil.