Greetings, and welcome to the Bogley. We call this stuff Canyoneering, and I hope you are aware that the Subway is not a "trail" (ie, does not meet the high standards for a trail in a National Park) but is a "route", requiring more backcountry savvy than the paved, well-marked trails found in Zion.
I think I have quite a good write up on the Subway here:
http://www.canyoneeringusa.com/utah/...zion-top-down/
Some people (ie, males age 17-30, and Jacob) do it without technical gear, but most will want a short rope (60 feet), harnesses, rappel devices and helmets. (Bickering will commence on this issue, here on Bogley).
There are three starts to the Subway from the top. The regular route is called either "the regular route" or "the Russell Gulch approach" since it goes NEXT to Russell Gulch. The second route is called Russell Gulch since it goes down Russell Gulch, and has three nice 100' rappels. A more-difficult route in is called Das Boot, requires wetsuits (probably) and has challenging navigation. For your first subway, I'd recommend the regular route. If your party is small and comfortable with rappelling, Russell Gulch makes a nice alternative with a little more action.
Das Boot and Russell Gulch require an additional permit thingee added to your regular permit (for free) and have a group size limit of 6. (Bickering will commence on this issue, here on Bogley).
It is super hot out, so wetsuits are clearly not helpful at the moment. There are swims so you will need drybags for anything you want to keep dry.
This time of year, is really, really hot out; so get an early start. The last 2-1/2 hours are along the stream in the full sun. We tend to take a siesta until about 5 pm at the end of the Subway section, then do the hike out when there is some shade on it. Which requires an extra lunch. There is not easily obtained drinkable water in there, but you could take a pump or Aquamira to get more water to drink.
And it is a Sublime route. Have fun!
Tom