Make sure your device is compatible with iOS 10. Compatible devices:
•iPhone 6 Plus
•iPhone 6s Plus
•iPod touch 6th gen
•iPad 4th gen
•iPad Air 2
•iPad mini 2
•iPad mini 3
•iPad mini 4
First do a backup of your device and data, to avoid data loss.
From your iOS device go to the Apple Beta page https://beta.apple.com/sp/betaprogram/ Click Sign up and sign in with your Apple account.
Accept the agreement.
Go to the iOS tab > enroll your iOS device > Download profile.
Follow the prompts to Install.
Your device will reboot.
Check for updates under Settings > General > Software Updates. follow the prompts to Download and install available updates.
Once completed you should be good to go.
You have to sign up for Apple's Beta Software Program. This will give you access to not only iOS betas but also MacOS betas. It will also give you a chance to give Apple feedback on any problems you might have with the beta versions. Go to this Apple website and click on the "sign up" button: