Apple has updated iOS to version 8.4 today and also put out the latest version of iTunes to match. You should be doing both because for better or worse iOS devices (iPhones, iPads) are still joined at the hip with iTunes.
It is important to update your iOS devices promptly because Apple wastes no time in invalidating previous versions. When iOS 8.3 came out a few months ago, Apple declared the previous version dead within days.
* If you only have the patience to do #2, Step 2 right now, please do it. At a bare minimum that is what you need to do right now. You can come back and do #1 and #3 later.
1. Local backup Once iTunes is Updated
Even though your iOS device is likely backing up key data to iCloud; it is not backing up everything. I like the idea of doing a routine (ex. monthly) backup of my iOS device to my computer. This can easily be done by plugging your device in to your computer. Within iTunes, click on the icon toward the top for your iPhone / iPad (why did you have to make this so confusing last year Apple?). Then click the Summary tab on the left for your device.
Toward the middle of the screen you will see a button that says Back Up Now. Click it. A manual backup to your computer will be launched. You may be asked to type in your Apple password at some point to back up your apps. This is a good idea. Go for it. This is your Apple ID / iCloud password.
After the backup is complete, you may quit / close iTunes and unplug your device.
2. Update iOS device
You can do this one of two ways — take your pick.
1. Since you know how to manage your device within iTunes, you can click on the Update button from within the Summary menu for your iOS device in iTunes (you will need to plug your device in again and open iTunes)
2. You can update directly from the device. You may have had enough of iTunes for today.
Settings >> General >> Software Update
3. Update iTunes (Check back in the afternoon / evening of 06/30 if not available)
Mac: Click the Apple menu (top left of screen), App Store (used to be called Software Updates). Do all software updates presented to you. Note: On a periodic basis, your Mac should be doing this automatically.
Windows: Open iTunes. Click the Help Menu. Check for Updates.