Click here for information on specific volunteer opportunities with the Episcopal Diocese of Louisana. The Diocese will provide you with the tools you need and with free housing, though you need to come up with your own transportation and food. Opportunities include gutting and rebuilding houses, helping with the mobile respite care unit (basically a distribution center, which I helped run for several months), community activities at St. Paul's or St. Luke's, helping with various soup kitchen or meals-on-wheels type programs, or traveling with the St. Anna's Mobile Medical Mission (a free RV clinic). The current volunteer coordinators are Susan Foto (firstname.lastname@example.org) and Darlene Davillier (email@example.com). Contact them to set up your trip after you've read through the ODR's website.
If you're intersted in a long-term internship, Foto and Davillier might be the people to contact, although you might also try Katie Mears, who runs the gutting/rebuilding program, at firstname.lastname@example.org. It can't hurt to include them all in the "to" field. Interns lead gutting and rebuilding crews, live in a house uptown, and recieve a small stipend.
I've provided detailed contact information for the ODR because it is the outfit I myself worked with. There are a number of other solider volunteer groups, however, and I'm sure you can find contact information at their websites:
Specific Volunteer Jobs at Volunteermatch.org
Evangelical Free Church of America
Presbyterian Disaster Assistance
United Church of Christ Volunteer Opportunities
Hands on New Orleans
Hands on Gulf Coast
(Much of the Dartmouth volunteering is done through the Hands On network.)
Common Ground Collective
For more information - My Blog Entry on Common Ground
Habitat for Humanity