connection to sql server?

Hello. Sorry if this is a novice question but can anyone show or point me
to some code in having windows authentication to sql server for an
application where it's not using just one generic windows account? I need
to assign individual windows logins to our users (basic authentication in
conjunction with https since not everyone is on the same domain). I notice
in pretty much all the examples/samples I see on the net they have the apps use 1 generic or surrogate windows connection to sql server
that's on the same domain but how does one configure the app to
allow individual windows authentication for users to access the app
from anywhere on the web? The reason I'm asking is because I need to use
SQL Profiler in seeing who did what to the data at what time, etc...

Thanks in advance.