Safari and Chrome Upgrade Instructions
Safari - OSX Upgrade
To upgrade your Safari browser, you will need to upgrade your OSX to the latest version, El Capitan. The newest version of Safari is part of this bundle. This can take a long time depending on your internet connection and you won't be able to use the machine while it is upgrading so best to do after hours or overnight.
Chrome is not bundled in an OS update like Safari. This is a link to Google's own instructional page on updating Chrome: https://support.google.com/chrome/answer/95414?co=GENIE.Platform%3DDesktop&hl=en&oco=1
Here is also another video that a youtube user created to help illustrate how to upgrade chrome.