There are many ways to get involved with HOT. The easiest first step is to join our mailing list: http://lists.openstreetmap.org/listinfo/hot. If you already know how to add data to OpenStreetMap then just start helping when there is a remote response. There are usually tasks involving tracing satellite imagery, looking over data and updating the wiki. This is coordinated through the OpenStreetMap Wiki and the HOT mailing list, as well as local lists depending on if the affected area has an existing OpenStreetMap community.
If you’ve never used OpenStreetMap before then the easiest way to start is by mapping your own community. Start by signing up for an account at OpenStreetMap and then zooming to the area around your house. You will probably see information that is missing, just start adding! Maybe there is a local OpenStreetMap meet-up around, go to their events it is a great place to learn more about the OpenStreetMap project in general.
Another way to get involved is by completing tasks on our Tasking Manager. The Tasking Manager divides geographic regions into squares and allows you to pick an area to work on. When you have finished a task you can then write a note about it and mark it finished. This is a great way to get started if you aren't sure what needs to be done.
A frequently asked question is how to get involved in work actually traveling to places to help with OpenStreetMap. Traveling to work in an area post disaster isn’t for everyone, the conditions can be tough. Also depending on the project HOT is currently working on different sets of skills that may be required. The best way to get involved in this capacity is by first being involved remotely. If you aren’t already involved in some capacity with OpenStreetMap it is unlikely you’ll be joining us to do fieldwork, unless you have a specialized skill required for a project. Additionally sometimes HOT has internship programs where you can go study with a team working in the field for a week or two and learn our techniques. Eventually we hope to have training camps to make it possible for more people to learn.