How do I lay asphalt shingles on a roof, and what should be under them?
Asphalt shingles by themselves will keep out the rain.  Extra steps increase longevity.  You need to follow the manufacturer's directions (take photos!) if the warranty is important to you.

Careful preparation can double the installation time and increase the cost by 25%.  Whether it's worth it to you depends on how catastrophic a leak would be.  For me, my garage or shed gets minimal preparation since a leak doesn't matter that much - it can be patched when it stops raining.  For a house or any finished space like a nice studio, a leak will mean ruined drywall, etc. so more attention is warranted.

In order from minimal work to a complete, nice job:


Minimum is a double course of shingles at the bottom of the roof.  The bottom course should be upside-down with the tabs cut off.  This is the minimum I'd do, maybe for a shed.
Next up is covering the roof with roofing felt before installing the shingles.  This increases the longevity of the shingles and helps the nails hold. I'd do this for a garage.
Best, if you're in a cold climate, is covering the roof with roofing felt then adding a 4' course of ice dam, which is a self-adhesive rubber membrane, at the base of the roof.  This helps prevent ice dams from damaging the shingles.  I'd do this on any roof over a finished space.


The shingles are not self-adhesive, but you'll see strips of tar on the backside.  After you nail the shingles down, the sun will melt these strips and adhere each course of shingles to the one under it.

One thing about the double-course of shingles that you start the roof with. The reason you cut the tabs off and reverse the shingle is to get that strip of tar at the very base of the roof.  The tar will melt and glue the first tabs down, helping prevent the wind from getting under the shingles.  For some reason many people I know, including my father who I worship, will put an upside-down course of shingles first without cutting off the tabs, to save time I guess. To me this is pointless since it does not do its job, which is to lock down the tabs at the leading edge of the roof.