Read the first bit of this carefully... https://docs.moodle.org/dev/Moodle_3.5_release_notes
Significantly, you need to first upgrade to Moodle 3.1. So read https://docs.moodle.org/dev/Moodle_3.1_release_notes carefully for that step! Also check server software versions - especially PHP. Then you can upgrade to 3.5. Take backups at each stage.
Some people advocate upgrading through each Moodle version. I don't see any point in this. 3.0.x -> 3.1.x -> 3.5.0 should be fine.
Awesome thanks so MUCH howard!
Actually.... you need to upgrade to <=3.4. You can't go straight to 3.5. Check what PHP version you have and what you are prepared to upgrade to (if you need to) and pick the intermediate version that makes your life easy
