SP will be added when either of these things happen:
-a skill completes
-you pause your skill training
-you add another skill to your skill queue, or other wisely makes changes to your skill queue, causing it to update by hitting the 'apply' button in the skill queue window.
However, with programs like EVEMon, you can view your total SP in real time, without making changes to the game itself.
how SP is calculated clone-wise, i'm not sure, but i would imagine clones working on total amount of SP, regardless of what your total SP appears to be in your character window.