When someone invites you to a Cocoon, they should provide a six-letter key. This is what you enter on the screen shown below . If you can't find the key, double check the message they sent you (either via text or email). You should see the key in that message. If you can't find it, ask the person who invited you to send you their Cocoon key.
Below is an example of what the invite message looks like. You should have one of these from the person who invited you to their Cocoon.
Once you have entered your key, you will be taken to a confirmation screen where you should see the Cocoon you were invited to displayed. You'll see the name of the Cocoon, along with the other people who are in it. If it is correct, press the arrow button. If it is not correct, you likely entered the wrong key, and you'll need to press the back button to try again.