This is more generic Joomla question and 1.x branch is very old - the way that most of us just don't remember it. I would not like to give you wrong instructions, but generally:
1. Please make a backup - both files and database
2. If you can - install the backup locally (xamp, mamp, other to the rescue)
3. Search in google how safely do the upgrade
4. Do the upgrade (if you were able to install backup locally - do it locally to be sure you will not damage online site)
5. After upgrading to a newer version - upgrade template also.
This is just a basic walkthrough - do every stem in the way you could reverse it.