If you can't get anyone to answer the phone, I would drop by the place, say, on your way home from work or on your lunch break or something, to find out the details before the day of the test. Most places don't do their own drug testing; they send you to a lab or somewhere else, so showing up at the HR dept probably won't help. Try to find out the info in advance. They may want a list of your medications, or sometimes they even want to see the medications (I guess to verify that you have a valid prescription, in your name).
If they send you to a lab somewhere else, you could wear whatever you want. No one from the new job will see you. If they do happen to do their own testing, I'd suggest business casual attire. No need to dress like you do for an interview, but you don't want to look disheveled either.