You can find out information on getting a passport from the US Department of State website. Students should apply for this no later than December prior to travel to assure that they are able to fill out the proper paperwork needed before the trip and in case of delay.
What if I lose it?
While traveling, if a student loses his/her passport the following documentation must be provided:
For travelers age 16 and over, a photocopy of the passport is sufficient, in addition to the items indicated (a statement of loss or theft from a police station, passport application form (download from web site), 2 photos, cash/card for passport fee, and an adult witness with ID vouching for identity).  Our Leader Guidebook (Passports tab page 1) and our Student Guidebook packing list (page 7) recommend having the 2 extra photos; however, most embassies now have photo machines.

For students under age 16, the process is more complicated. In addition to the above, there are two additional requirements:
1. The leader needs a notarized authorization signed by custodial parents, and the notary should indicate the type/no. of ID that each parent provides.  If the parents are divorced, both most sign if they share custody, and if only one parent has custody, there must be proof of the court order  awarding full custody.  A sample form is attached if you want to have it done in advance for your students who will be under age 16 during the time you are abroad.
2. A copy of the student's birth certificate must be provided.
Both 1 and 2 can be sent abroad by fax, but if the parents can't be reached immediately, and the loss occurs at the end of the trip, it could be difficult.

The following web site gives more details:

Please note especially the following: It says to click on new rules for minors under age 14, but it should say under 16 . When you click, it goes to the page saying for minors under age 16.
Language & Friendship
Shannon Ruiz,
May 14, 2010, 12:50 PM