A tar.bz2 file is a compressed library of files. It is often non-compiled source code. If it is an application that means you need to compile the source code and then install the source code. That is quite high end computing which, under a MS Windows system would take you probably over 50 complicated mouse and keyboard operations in a overly-complicated GUI compiler environment, assuming you have purchased a >$100 MS compiler to do the job.
In Linux it is MUCH easier, but will have to use the command line to make it easy on yourself. Here are the steps
1) open a terminal
2) navigate to the directory where you put the .tar.bz2 file using the "cd" command
3) tar xzjf nameoffile.tar.bz2
4) navigate to the directory created by the previous command (usually "cd nameoffile")
7) su (then enter root password)
EDIT: from your previous postings you wanted to install OpenOffice. If the .tar.bz2 file you are talking is an openoffice one (you should have told us that in your initial question) then do only steps 1-4 above and then if there is a .sh file in that directory just run ./nameoffile.sh and it will install the product.