To participate in GeoNet you must have an Esri Account. Logging into GeoNet with your Esri Account established your GeoNet identity. If you are interested in having people participate in your group, you will need to understand how to invite both members and non-members to your group.
If someone has a GeoNet account, then you can use the invite action and select their name from the invite dialog.
If someone does not have an account, there a couple different ways that you can invite them to GeoNet.
Sending them an email
Send the following url for them to create an Esri Account: http://accounts.esri.com/signup
Once they have created and verified their account, they can log into GeoNet.
Share your group
Open and member only groups can be shared directly from the group page.
You can enter a person's email address, and if they do not have an account on GeoNet and email will be sent. Once they click the link, they will be taken to the group and will be given an opportunity to log in or create a new account.
For private and secret groups you cannot share a group or invite through the group. The simplest option is to send them the information on creating an Esri Account and have them log into GeoNet. Once they log in, you will be able to invite them to the group.