How to install iOS 7 Beta without UDID / Developers account:

Step 1: Launch iTunes and connect your iPhone with your PC via USB cable.

Step 2: Right click on your iDevice on iTunes and take a backup (or backup to iCloue)

Step 3: Restore your iPhone to iOS 6.1.3 (or 6.1.4 if you have iPhone 5)

Step 4: Set up as new iPhone - do not restore from backup.

Step 5: Hold down the Option key in OS X (Windows use Shift key) and click on "Update" not on "Restore"

Step 6: Select the iOS 7 beta file you downloaded, updating the device to iOS 7 beta. Done.