You browse folders on a command line very much like you do in a gui. In ubuntu when you open the terminal, your current working directory will be your "/home/yourusername" directory. Commands you need to know to browse/change working directory:
"ls" - lists all the files and folders in your current working directory.
"cd" - change directory, as in "cd xonotic" to change your working directory to the xonotic folder, in the folder you were previously viewing.  
"cd .." - will take you up one folder to the directory you were previously in.
Here's an example of how you might browse to your xonotic folder and run the game:
First, extract the game folder to your home folder, if you havent already. Open a terminal and observe the following commands (your paths/folder names will differ slightly from my own of course):
Code:
jaywalker@JayNix-Desktop:~$ ls
add-remove reconstructor list  examples.desktop  Nexuiz         Templates
AssaultCube                    FreeBasic         nvclock fan    Ubuntu One
BackInTime                     HALO              Pictures       umjnx.sh
BF1942.pid                     lmms              Public         UT2004
bz98                           mnjnx.sh          reconstructor  Videos
Desktop                        mprime            sauerbraten    www
Documents                      Music             Source         xonotic
Downloads                      My Games          Starcraft      xonotic-preview
jaywalker@JayNix-Desktop:~$ cd xonotic-preview
jaywalker@JayNix-Desktop:~/xonotic-preview$ ls
Xonotic
jaywalker@JayNix-Desktop:~/xonotic-preview$ cd Xonotic
jaywalker@JayNix-Desktop:~/xonotic-preview/Xonotic$ ls
bin64                 misc                       xonotic-linux32-sdl
data                  ogg.dll                    xonotic-linux64-dedicated
Docs                  SDL.dll                    xonotic-linux64-glx
fteqcc                server                     xonotic-linux64-sdl
key_0.d0pk            source                     xonotic-linux-glx.sh
libcurl-4.dll         vorbis.dll                 xonotic-linux-sdl.sh
libd0_blind_id-0.dll  vorbisenc.dll              xonotic-osx-dedicated
libfreetype-6.dll     vorbisfile.dll             Xonotic-SDL.app
libgmp-10.dll         Xonotic.app                xonotic-sdl.exe
libjpeg.dll           xonotic-dedicated.exe      xonotic-x64-dedicated.exe
libmodplug-1.dll      xonotic.exe                xonotic-x64.exe
libpng12.dll          xonotic-linux32-dedicated  xonotic-x64-sdl.exe
libtheora.dll         xonotic-linux32-glx        zlib1.dll
jaywalker@JayNix-Desktop:~/xonotic-preview/Xonotic$ sudo chmod +x xonotic-linux32-sdl
[sudo] password for jaywalker: 
jaywalker@JayNix-Desktop:~/xonotic-preview/Xonotic$ ./xonotic linux32-sdl
The very last command should run the game for you.