Whether you use a drop spreader, a broad (?) spreader, or even a little hand spreader like this; it's critical to get even seed distribution rather than spreading by hand. As to how much seed to use, you should definitely consult the bag. It's going to take a little math to figure that out, but most seeds, if you need a visual reference, will probably go down, with say, a quarter inch of space between the various seeds. You definitely do not want to put down too much seed because even though that sounds good, when the seeds sprout and become grass plants, they will be too closely spaced and compete with each other and eventually cancel each other out.
Then once your seed is spread, you need to make sure that the seed is in really good contact with the soil. There are several ways you can do that. If you've already prepped the soil pretty well and you have a light roller, you can sort of roll over to press the soil down and the seed. A lot of people don't really have a roller. Some of the ideas I've heard is to drag a piece of carpet over it, drag a broom lightly over it, or maybe you can even use the back of a leaf rake and just lightly go over the surface without moving the seed too much aside or making it ball up. It will just work the seed into the soil a little bit so that when it's wet, you'll have excellent contact between the soil and the seed and when the little root hairs come out of the seeds, it will be able to move right into the soil and start to grow a grass plant.