Before applying a new iOS update you need two things. Enough storage space on your mobile device for the installer and a good backup. Here are a few details about making sure your iPhone (or iPad) is backed up correctly.

On iCloud

Apple has gotten a lot better about backups for your device. They understand that everything on our phones is super-important and very personal. So, they offer iCloud backups directly from the device. You don't need to plug your iPhone or iPad into a computer to backup. It will usually complete a backup to the cloud any time it's plugged into power and on WiFi.

If you aren't sure that your phone is set to back itself up to iCloud every night, look in Settings > iCloud > Storage & Backup > Check to see if iCloud Backup is turned on, and when the last backup was completed. If you are out of storage space in iCloud, tap on Manage Storage in that screen and start removing apps and data that's less important. If you are a family all using the same Apple ID and iCloud account, you will probably need to upgrade the storage plan. The newest prices (October 2014) are more reasonable at only $1 per month for 20GB. I recommend the larger iCloud plans because of how incredibly useful iOS automatic backups are. For me 20GB barely covers the backup requirements of 4 devices.

On your local PC or Mac

If you don't want to use the iCloud backup, just plug your phone into any computer running iTunes. You can configure backups in iTunes when the phone is connected, and you can trigger manual backups in that interface. You should turn on encrypted backups in iTunes because this option will store a lot more useful information (like email accounts and wifi password) than the unencrypted backups store.