1- First, please make sure you have filled-in the Beta program subscription form. If you don't have the link to this form, here it is.
2- One day after your registration, you will receive an email from iTunes on your email address associated with your Apple ID. Please make sure to check that exact email box with your iPhone/iPad. You should find there an email from "TestFlight" with the following object:
Make sure to check your spam folder if you don't find anything in your inbox. In case you find no mail, contact us at firstname.lastname@example.org and we will send you a new one.
3- Click on the button 'View in TestFlight'. If you don't see the picture below it probably means that you didn't open the TestFlight email on your iPhone/iPad but on your computer instead.
4- Copy the personal code that appears (the area framed in red in the picture below). You will need after that to download TestFlight application which handles beta versions on your phone, and to paste the code that you received.
5- Download TestFlight from the App Store if you haven't done it yet, open it and click on 'Redeem'.
6- Enter the code that you've already copied and click on "Enter". Wait for the beta version's download to end.
7- Congratulations, you can now test the beta version !