I use the Connect App on an Android operating system phone, so based on that bit of information here is how I can add people to a group.
With the Connect App open and the Contacts option selected, in the upper menu bar I can click on the plus sign and select New Group. I enter the new group name and select the OK option. At that point the app takes me to a list of my contacts where I can click a check box to the right of the name to add people to this new contact group. When done with my selections, I click the Create Group button at the bottom of the screen.
To add contacts to an existing group, select the group which will take you to a screen listing the current contacts. At the top of the screen there is an Add to Group option, and selecting it will open up a listing of your contacts with a check box to the right of each name to allow you to select additional contacts. When done with your selection, click the Add To Group button at the bottom of the screen. The additional contacts will be added to the group and you will be taken back to a listing of contacts that are in the selected group.
Hope this information helps you out