If my board is locked down on one end (for example, through using the second screw hold on the siding clip), how much space do I need to leave on the other end to allow for expansion?

This depends on the length of the board. An 8-foot board would need 1/8th of an inch, a 16-foot board would need ¼ of an inch, and a 32-foot span (two 16 foot boards in a row butted up where they meet) would need ½ an inch.