There are two ways you can be invited to a channel; a text message to your phone number or by email. If you are accepting an invite via your phone number just follow the instructions in the text message you received. If you are being invited via email, you will want to make sure you open that email on your mobile device and then just follow the instructions therein as pictured below:
Note: Invites will expire after 5 days, so be sure to keep your eyes out for them. If your invite is not working, just reach out to the leader of the channel and they can get another one sent to you!