I don't know if this is a 'proper' way to do it (I don't know java), but it seems to work (for my desktop anyway)...

import java.net.InetAddress;
InetAddress inet;
try {
 inet = InetAddress.getLocalHost();
 println(inet);
}
catch (Exception e) {
 e.printStackTrace();
}

edit: probably worth noting that (if I understand this right) in the above example, 'inet' is of type InetAddress, not a string. So you'll have to convert it to a string (and extract the IP part) to use it with processing.net's Client objects.

Found it here:

http://java.sun.com/j2se/1.3/docs/api/java/net/InetAddress.html