I'm in the process of installing an 8-ft high wooden picket fence, the
type that has 1x8 slats with barely a seam between them, which are fixed
unto 4x4 posts set some 10 to 12 feet apart. My question has to do with
the easiest way to align the bottom (or the top) of the slats so that
they follow a straight line between posts, and not contour the land.

Do I simply tie a string or line to each end post and make sure it's
perfectly level, then align the bottom of the slats to the string? Or do
I simply line the top of the slats with each support and end posts, mark
them with a pencil, and use that for the alignment? Have no experience
but I'm willing to experiment until it looks right (and straight).