If you double-click on (allow-executing-file-as-program) start-tor-browser, you should be presented with a dialog of four options: Run, Run-in-Terminal, Display and Cancel. Do you see these options? If so, try Run.

Alternatively, you can set up a custom keyboard shortcut and use something like the following command (depending on where / into which folder you extracted tor):

"/home/user_name/my_tor/bundle/tor-browser_en-US/start-tor-browser"

to launch tor.

(Don't use sudo.)

If you wanted to launch tor via the command line, you could navigate to the folder and just type start-tor-browser. Given that it's just locally downloaded and not formally installed, you'll need to supply the path (or register start-tor-browser manually - but that's a separate question).

Update (mid-May 2015)

The previous command ceased to work for me. The following does work:

sh -c '"/home/user_name/where_i_put_tor/bundle/tor-browser_en-US/Browser/start-tor-browser" --detach || ([ !  -x "/home/user_name/where_i_put_tor/bundle/tor-browser_en-US/Browser/start-tor-browser" ] && "$(dirname "$*")"/Browser/start-tor-browser --detach)' dummy %k

_{... taken from the official Tor desktop configuration file ...}