One question to resolve first is... can a User belong to more than one
group? For example in my church-membership database I can be simultaneously a member of the Deacons, the Choir, the Ushers and so on; or you might have the simpler situation where every User belongs to one and only one group (at a time, and you don't want to keep the history).
If it's only one group, then all you need to do is create a Groups table; it should have a Primary Key (the GroupID, which might be an autonumber or a short, stable text code) and then perhaps some other fields for information about the group as a thing in its own right (a descriptive GroupName text field for example). You would then simply include a GroupID field of the same size and datatype as this Primary Key in the Users table.
You would then use a Form based on Users (never use table datasheets for routine interaction with data, always use Forms) and put a Combo Box control on the form to choose the group.
Post back if it's a "many to many" (one User can be in zero, one, or multiple Groups and each Group can have zero, one or many Users); this is very common but requires a third table and a bit more work.