Hello prudens (wise one)
Have you decided what language to use? Bash shellscript is suitable and easy to debug.
The easiest way to approach software development like this is to take it in bite-sized chunks and do each step manually, for familiarisation, before linking them all together in a script.
You could start by doing the tar and FTP parts at the command line. Man pages are good references but not the easiest introduction. I've been using *n*x systems a while and I still go looking for examples (HOWTOs and FAQs) on the Internet if the man page does not make sense straight away.
Here's a page exampling tar
There are lots of FTP HOWTOs and FAQs so Google for FTP HOWTO or FAQ and pick the one you get on best with.
The environment your script will eventually run in, set up by cron, is different from the login environment and this often causes breakage. In particular, the $PATH variable is different so safest to use full paths for your commands, example /usr/bin/ftp rather than ftp.
You may also like to include a date in your tar archive (output) file name so you can store several on ftp.linuxrulez.com. That way, if you find you want a file that was deleted a while ago you can get an old tar archive and restore it.
When you come to scripting the FTP put (upload) you will probably want something like
ftp $host_name <put_script>> put_out 2>&1
This feeds whatever is in file put_script to the ftp program, the same as when you are entering the commands at the terminal by hand. All the output from the ftp command is sent to file put_out which will be a valuable troubleshooting aid.
When (if?) you get stuck or want feedback on whether you are doing things the best way, post what you've done here. It's easier to read your stuff if you put it in CODE tags, that's the word CODE in brackets  to begin and /CODE in brackets to end.
Looking ahead to when you've got it working I strongly recommend that you also get your backup file from ftp.linuxrulez.com and test that it can be used to restore files; many people have only found out that their backups don't work when they try to restore from them!
Finally, your backup script may fail; if it writes a log and you can discipline yourself to check it regularly then you will avoid the danger of thinking the backup is working until you need to restore something and find the script wasn't working for the last few months!