Fasten with Drywall Screws or Drywall Nails?
You are probably not going to hear a convincing, or at least conclusive, argument on either of these. Yes, screws are more secure, but nails cost less and are easier to install in most cases. You really have to look at the job, but just know you really can't go wrong with either.
Ceilings- OK if there is one place you really should use screws it is when installing drywall on a ceiling. Gravity is working against you 24 hours per day. Let's just be safer and use screws.
Regular Walls- This is where the playing field evens out. Screws cost a little bit more, but many building codes require twice as many nails per sheet of drywall than screws. Since drywall nails are not twice the price of screws it's a no-brainer, right? Not so fast. How are you going to screw in those drywall screws? You'll need a screw gun. Those aren't free... unless you already own one or can borrow one. Drywall hammers are only a few bucks and screw guns are about ten times that. In many cases this could be the deciding factor, especially if it's a small job and you don't own a screw gun.
What Size Screw/Nail?- You can always go a little longer than needed, but NEVER go shorter than recommended. If you are using nails its always a good idea to spend a few extra pennies and get the annular/ring shank type nails (they are "ribbed" with rings for better grip and will resist pulling out). For 1/2 inch drywall you should use at least 1 1/4 inch length screws or nails. For 3/4 inch drywall you can go at least 1 1/2 inches for nails and a little shorter 1 3/8 inches for screws.
Sinking and Fastening- Try not to break the paper... but it happens. When you do, it will lose holding power. It's not the end of the world if you mess up and need another screw/nail right next to a bad one. If you bend a nail, just pound it all the way into the drywall. Don't pull it out. You want to make an indentation in the drywall paper with screws. With nails, you will want to leave a little round dimple in the drywall from the hammer head. These dimples and indentations will be filled in and smoothed over with compound.