Simple question (I guess): 555 timer
If you use a P-channel MOSFET to switch power, and use a button to turn on a timer, which, when done, releases the gate of the P-channel (pull it up to power-in with a resistor,) you will have a circuit that draws no current when off (well, maybe a microamp or two.)

I'd solve this by a small MCU like an ATTINY-85, but it could likely also be done with a 555 in one-shot mode.







simulate this circuit &ndash; Schematic created using CircuitLab

For a small-current circuit, a cheaper P-channel MOSFET than the SUP75P03 can be used -- something like a BS250 might even be sufficient if current draw is &lt; 100 mA or so.