You will need the Limited Read People permission to see this information.
Navigate to the person's profile and click on the Involvement tab. Then select the Groups subtab.
All groups the person is currently a member of will appear in a table with such columns:
Group
Type
Category
Leader(s)
Member Type
Positions
Start Date
Other columns that can be included are
ID
Record Type
End Date
Date Last Attended
Notes
Custom Fields
The Leader Name(s) column lists everyone serving as an admin or leader for that group, so you don't have to open each group to find out who leads it. See What is a Group Admin and Group Leader? for more on these roles.
Note: Add the Leader Name(s) column if you regularly need to know who leads each group a person belongs to — it saves you from checking every group record individually.
You can use the Start Date field to filter the groups based on which groups the person was a member of on that specific date.
You can click on an individual group to look for information relating to that group.
The fields that appear under a group are all the custom fields defined on a group membership profile (if any).
The following actions are available.
You must have the Write Full Groups permission to perform these actions.
Edit - edits information related to the person's membership within the group.
Remove - completely removes this person from the group. If you would rather drop them and keep history, edit the record instead and add a drop date.