To update Joomla 1.5 to its latest version there are few steps you should follow:
- First, download the appropriate update package from the official Joomla website
- Extract the files from the archive you have just downloaded
- Upload the new files overwriting the old ones.
NOTE: Make sure you have created a backup of your website before you overwrite your old files.
Alternatively, there is a free Joomla component that does all this for you. It is called jAutoUpdate and you can download it from the Joomla Extensions Directory. It will save you all the hassle to download, extract and upload the new files again. All you have to do is click a button and your application will be up-to-date!