What I wrote above is a series of commands that you put into a terminal window. To open one, hit the start button, type 'terminal', then click the terminal app. You should get a text window. This is similar to a cmd window on MS Windows.
Then you can start typing the commands above. Here's what they do:
Download the file:
wget http://softlayer.dl.sourceforge.net/project/bitcoin/Bitcoin/bitcoin-0.6.2/bitcoin-0.6.2-linux.tar.gz
Now it's in your home directory. A .tar.gz is like a zip file. To extract it we use the tar program:
tar -xf bitcoin-0.6.2-linux.tar.gz
Now your home directory has the tar file plus the bitcoin directory. To see everything there, type 'ls', which is like 'dir' in a cmd window.
Next you go into the directory where the program is. 'cd' means change directory. The program is three levels in, so:
cd bitcoin-0.6.2-linux
ls
cd bin
ls
cd 32
ls
Above I just shortcutted you in like this:
cd bitcoin-0.6.2-linux/bin/32
Either way works. Then you have to run the program. Unlike windows, the current directory isn't in the PATH on Linux, so if you want to run a program you have to prepend './' . Thus:
./bitcoin-qt
And the program should start.
If you prefer to work with the GUI, you can do it that way too. First use Firefox to download the .tar.gz . It will save it to your Downloads folder. To get there, click the file folder icon on the left. Click the bookmark for Downloads. You'll see the .tar.gz. You can drag it to your desktop if you'd like. Right click and choose "Extract here". You'll see the new folder appear. Double click it, then 'bin', '32', 'bitcoin-qt'.