The key to successfully turning seed into established grass is consistency and awareness of how you water it. For the first 1-4 weeks, or until the seed has germinated, water lightly (mist or fine spray) 1-2 times per day to keep the top inch of the soil consistently moist. Do not wash away the seed with too much water. After the seed has germinated, continue to water daily, keeping the top 2 inches of soil moist until the grass reaches mowing height (about 3 inches). Once the grass has reached this point, you can reduce watering to roughly twice per week, but soaking the soil more deeply. The goal during this stage is to encourage roots to grow deeper into the soil.
The straw matting put down over new seed does NOT need to be removed. The matting will disintegrate, and is not only a protective shield for your seed, but also prevents erosion, which will wash away the soil and seed. Once the seed grows in, you won't even be able to see the matting!