A simple get you up and running...
I'm going to assume we are working in your 'USERNAME' home folder. I'm going to call it wali ie;
/home/wali
Now change directory to your downloaded files. This should be where your file was naturally downloaded to. Open a terminal can cd to that folder ie;
cd ~/Downloads
that should leave you in the directory
/home/wali/Downloads
then extract that file with this command
unzip -xzf fritzing-0.9.3b.linux.AMD64.tar.bz2
then change to the fritzing working directory ie;
cd /home/wali/Downloads/fritzing-0.9.3b.linux.AMD64/
The exectute fritzing
./Fritzing
or
sh Fritzing
You should be running @this point.
The main program is compressed for many reasons, an uncompressed file is just not feasible for the average internet users bandwidth. Why download 350+mb when it can be done in 174mb? Occam's razor good sir. As the simple answer is usually the best one. Hence a compressed file.
Good luck!