This isn't a very simple question to answer because it's so broad and involves several different operations.
User Credentials
On startup you need to check some sort of storage (e.g: SharedPreferences, Database) for a username/password.
If none exists, you'll need to prompt the user to enter their username/password so you can capture and store it somewhere (e.g: SharedPreferences, Database)
Shared Preferences Tutorial
Database Tutorial
File Updates
File Modified Date - Before deciding whether or not to download the file, you need to know when it was modified. This should help: Android: how to know file located in web server is modified?
Determine if the file is newer - After you get the last modified date of the file on the server, you need to compare it to the modified date of the file you currently have. I would suggest that whenever you download a file, you save the modified date (retrieved above) in some sort of persistant storage (Database, SharedPref).
Downloading the File - Here's a tutorial that should help if you decide you need to download the file on the server.
http://www.hassanpur.com/blog/2011/04/android-development-downloading-a-file-from-the-web/ - A bit complicated, but it also does the download on a background thread, which is a good idea.
Pretty vague answer, I know, but it was a pretty broad question. If you have a more specific question, we can give you a better answer.