Today Apple released iOS 8.0.2 which brings lots of bug fixes for a variety of issues such as broken HealthKit, MMS/SMS issues, problems with third-party keyboards, and problems uploading images in Safari. iOS 8.0.1 was released yesterday but then immediately pulled because it caused significant problems for iPhone 6 and 6 Plus users.
To update your phone first make sure you are backed up.
- iOS 8: Settings > iCloud > Backup > Backup Now
- iOS 6 and 7: Settings > iCloud > Storage & Backup > Backup Now
Then go to Settings > General > Software Update.