Mailing list groups are tricky in Windows 8.1. In fact, so far, the Mail and People apps don’t allow you to create a group. Instead, you have to log into www.outlook.com, then choose People from the little drop down arrow next to the word Outlook.
In People (on the Web, not in the app), New has its own drop down arrow for Group.
Once you have a Group, you add existing contacts by name. (That is, you cannot create a new contact and assign it to a group in one step.)
If you want to add a member to a group later, select the group, then select Edit. Add members one at a time.
Just as you can’t (yet) create Groups in the People app in Windows 8.1, you can’t use the group in the Mail app (perhaps this will change with an update this year), Again, the solution is to browse www.outlook.com. Start a new message and type the name of the group in the To box.
If you spend a little time with outlook.com, you may find it preferable to the individual apps in Windows 8.1, although the latest Mail app actually has a few features lacking on the Web (pinning contacts, for example).