Dynamite is relatively common, and can be found - or stolen - in many places in the wasteland. Military facilities often stock dynamite, and mining operations of any type often carry supplies. Dynamite is also a somewhat common item in shops, and can be purchased for reasonable prices with a decent Barter skill.
Dynamite has a timer that can be set to anywhere between 10 seconds and 3 minutes, in 10-second increments.
In Fallout, dynamite must be dropped manually, even if held in the active item slots. In Fallout 2 however, if they are activated in the active item slots, they drop automatically.