I use Linux daily, but not Ubuntu's Unity interface, so I can't help you with what to click in Unity.
I can help you with the commands to type in a terminal window, which is basically the same on all Linux distros. Can you run the terminal program?
First, type this:
cd ~/Desktop/
That will change to the Desktop directory where you've downloaded all this stuff.
Before getting starting, you might delete everything you've already tried, so you're starting from a clean slate.
You need to download Arduino 1.0.2. The new 1.0.3 is not supported yet, so be sure to get version 1.0.2. Get it from
www.arduino.cc. I can't tell from your screenshots if you're running 32 or 64 bits, so you'll need to figure out which version you have and then download the correct one.
Likewise, since I don't know which version you have, I have to make an assumption in these commands. I'll assume 32 bits. If you're using 64 bits, change these commands slightly for the filename with 64 bits.
After you've downloaded Arduino 1.0.2, type this command to extract it:
tar -xvzf arduino-1.0.2-linux.tgz
You'll see an incredibly long list of files print very rapidly.
Next, download the Teensyduino installer. It's available here. Make sure you get the one which matches your system (32 vs 64 bits):
http://www.pjrc.com/teensy/td_download.html
By default, the file will not have executable permissions. So type this command to make it executable:
chmod 755 teensyduino.32bit
Again, I don't know if you have 32 or 64 bit, so if you're using 64 bit, change this command to match the file you downloaded.
Then, to run the installer, type this:
./teensyduino.32bit
Click "Next", until you get to the part where you have to select the copy of Arduino to modify. Since this is all in your "Desktop" directory, double click it, and then highlight "arduino-1.0.2". The instant you highlight a copy of Arduino, the Next button will enable. Keep clicking Next until the install is done. You don't need the optional libraries, and if you later decide you do need some, just run the installer again to add them.
After you've finished the install, go back to the terminal window and type:
cd arduino-1.0.2
Then type this to run it
./arduino
You should see the Arduino window appear. The first thing to do is select Teensy 2.0 from the Tools > Boards menu. Then use File > Examples > 01.Basics > Blink to open the blink example.
Unfortunately, there is 1 more step needed on Linux. You must download and install (merely copy to a certain directory) the udev rules file. I described that above. If you don't have the rules file installed, everything will work up to this point. But when you click Upload, the Teensy Loader window will appear, but it will be unable to detect your board.
Hopefully this helps? There's probably a way to do all this stuff from within Ubuntu's Unity GUI, but I've never used it, so I just can't direct you on what to click. The command line within the terminal window can do everything, and the commands are essentially the same for all Linux systems.