To hike the Subway, you must apply for a lottery permit at the Visitors Center or online a few days before your planned hike. If you win it, you pick it up at the Visitors Center the day prior. This permit is crucial - it's a $175 fine a person if you hike without it.
The hike starts on Kolob Terrace Road, just outside the main park. You'll hike down until you enter the canyon, at which point you'll need to put on your water shoes and unload your rope to climb down three somewhat perilous points.