You can define how information is passed to SQL when you define the connection. For example, if you are using Access for a front end, click File, Connection then option 2 defines how your users connect to the database. SQL will automatically retrieve the NT login info, so you won't have to worry about it.
The users do need to be defined in the SQL database of course. The easiest way I've found is define an NT group with the proper permissions, and you won't have to put each individual user in. Remember to define the group or users as <Domain>/<NTUserName>.