If you want to use a single account, you need to have your .net application use impersonation, so that it connects using an impersonated windows account.
Otherwise you could create a Login (and user) for an AD group and add your AD users to that AD group. Then the users would be able to connect to SQL server using their credentials, without having to give each them their own logins.
Excuse my typos and sometimes awful grammar. My fingers work faster than my brain does.