Picture from flickr by Windwirral
Here are the basic steps to use tar and gzip to package up some files in a compressed archive, so that you can move them to another computer or back them up.
First you want to create and add files to the archive. Go to the target directory and enter individual filenames and directories you want to have included.
tar -vzcf mystuff.tar.gz file1.txt file2.doc mypictures/
Now you can test if that worked by listing the files in the archive.
tar -tvf mystuff.tar.gz
When you want to extract the files, go to the folder where you want to extract them, in this case 'targetfolder'.
tar -vxf mystuff.tar.gz