Question
How long do I let a grocery store bought peach seed dry out before planting?  Can I start this seed in a flower pot?

Answer
Your Peach Tree -- Prunus persica to Botanists -- is hardy to Zone 7.  If you live somewhere there or South, you can grow your Peach outdoors.

Scrub your Seed well and soak overnight in fresh water to remove all traces of the pulp..  These seeds need exposure to freezing temps to be able to germinate -- several months of 'cold stratification'.  They need to be sitting in your freezer until August or later, in a plastic bag, where the cold air will prepare it for the warm-weather growth that follows.

You'll see some good details in the Wikipedia Encyclopedia online:

http://en.wikipedia.org/wiki/Peach

where they have several good points for growing these from seed: 'Peaches should be located in full sun, and with good air flow. This allows cold air to flow away on frosty nights and keeps the area cool in summer. Peaches are best planted in early winter, as this allows time for the roots to establish and be able to sustain the new spring growth.'  There's more to read once your Peach Tree reaches puberty.  Let me know when you get there!  Save me a Peach, I'll get you a good recipe for Peach Pie!