I want to be able to login via a .NET app using a custom login page on my app so I want no redirection to the salesforce login page. I want the process to be internal. So how can I implement a way that would allow me to retrieve the security token from the API using the login and the password that a user would input in my login page? If that's not possible, what other ways can I use to keep the login process stricly on my app and just use the login and password?
You would call login(). To do this, go to Setup > Develop/Integrations > API, download the Enterprise or Partner WSDL, import the WSDL in to your IDE, and call the login method from the client stub. The resulting session ID can be used for basically any type of API call, including REST and SOAP calls.