To add multiple people (also referred to as "Adding people in bulk") to groups you can use the self-importer to import a spreadsheet where you have a column for group membership. 

You can also use the self-importer to add people to campaigns in the same fashion, you'd just want to make sure that you have the donation details as the system won't add people to a campaign without a donation record. 

Here's a quick walk through that shows you how to add multiple people to a group at once:

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