There are mainly two ways to use JDBC – using Windows authentication and SQL authentication. SQL authentication is probably the easiest. What you can do is something like:
String userName = "username";
String password = "password";
String url = "jdbc:sqlserver://MYPC\\SQLEXPRESS;databaseName=MYDB";
Class.forName("com.microsoft.sqlserver.jdbc.SQLServerDriver");
Connection conn = DriverManager.getConnection(url, userName, password);
after adding sqljdbc4.jar to the build path.
For Window authentication you can do something like:
String url = "jdbc:sqlserver://MYPC\\SQLEXPRESS;databaseName=MYDB;integratedSecurity=true";
Class.forName("com.microsoft.sqlserver.jdbc.SQLServerDriver");
Connection conn = DriverManager.getConnection(url);
and then add the path to sqljdbc_auth.dll as a VM argument (still need sqljdbc4.jar in the build path).
Please take a look here for a short step-by-step guide showing how to connect to SQL Server from Java using jTDS and JDBC should you need more details. Hope it helps!