I have a single 15 amp breaker available in my pool electrical panel. I would like to run power from there to my shed for a handful of outlets and a pair of light fixtures. I plan to bury metal conduit 6" deep, but beyond that I'm unsure what is required. Do I need a subpanel or disconnect in the shed? What size and quantity of wires would be required in the conduit? The shed is about 45 ft from the pool panel. Do I need a grounding electrode at the shed? This is in the state of Georgia, USA.
Go ahead, but make sure to get the details right
Since you are pulling 25A (out of the 40A total available) on the pool feeder right now, you can route a single 20A/120V circuit (using 12/2 W/G UF or 12AWG THWN hot/neutral/ground in the conduit) from the pool subpanel's spare breaker to a disconnect at the shed (any standard A/C disconnect box will do the job happily), then you can wire the shed lights and receptacles to the disconnect box as they won't consume but a fraction of the remaining 15A normally.
You won't need a full subpanel at the shed since you're feeding it with a single branch circuit, nor will you need a grounding electrode as you are installing a disconnect for a single circuit, not a feeder and subpanel. (This is per the exception to 250.32(A).)