Hi
For start I would make a backup of the site and test it on copy first. Make sure You have error display activated on site and server, so you will see all problems, than update joomla using a joomla update option or by installing a package. I guess some of the outdated extensions will make joomla collapse, so just look at errors and rename all the folders it's mentioning to something else (I'm always adding "_" in front of old folder name). All of this extensions will need to be updated as soon as You will see joomla working.
You can also use one of Joomla Migrate extensions.