Obviously the easiest way is for invites to be open, you get the invite and register your account during the open period. Good luck with that.
There are other ways in though, but you have to be persistent. The most common way is to have a registered user share an item with you to get in. Every step of the way is hit or miss. You may or may not get an email indicating that someone shared something with you.
If you do get the email, click the link to see the post, there will be a join button. The join button may or may not get you in. If it does not, bookmark the page and come back to click the join button often.
If you have an android phone, install the app and periodically try to login to the service. Do it often, I know a few people who got in without a share or an invite.
The key is to keep trying to login/register. Many of the people I have gotten in never received the notification email, one of the times they tried to get in it just worked.
If you have an account, it's not a bad idea to make a circle just for people who have not gotten in yet. Share stuff with this circle from time to time until they get in, most people I have invited got in this way.