To begin, log into your Office 365 site using an Admin
account.

From there, open the Settings
menu.  Select Site Settings.

Next, under Users and
Permissions, click on People and groups.

Select the
Group name which you would like to
add a user to.  From that group’s page, click
on the New (+) icon.

A pop-up will appear asking you to share the site with the
user.  Enter the name(s) of the user(s)
you would like to add to the group (for more on how to create a new user, see Creating
New Users on SharePoint Online, Part 1: How to Create a New User Click ).  Once you have entered in the name(s) of the
user(s) whom you would like to add, click on the Share button.

Once the user has been successfully added to the group, you
will see their name listed under the Group
name.  To verify that the user has
been added, have him log into the site and try to access the group.