How do I stop domain users having to log in when accessing SP foundation?
Is the site in the local internet zone in the browser (I assume it is Internet Explorer)? Then you should verify the settings at:
Internet Options / Security / Local Intranet / Custom level... / User Authentication - it schould be
Automatic logon only in Intranet zone
Otherwise you can set this value for other zones as
Automatic logon with current user name and password
although that is not considered to be secure.
You should of course test the settings first on a single PC, then set it (or let the user set it) either manually on each other, or push the changes via Policy (I assume the PCs are part of an Active Directory domain) or maybe via a login script.