How do I make this routine generic so that I can connect to any type of database?

public SqlConnection GetConnection()
{

    // Define variables
    bool bTrustedConnection = true;
    string sDatabase = "test";
    string sPassword = "";
    string sServer = "PC108\\SQLEXPRESS";
    string sUserName = "";

    // Define variables
    string sConnString = "";

    // If the user is trusted...
    if (bTrustedConnection)
    {
        // Create the connection string for a trusted connection
        sConnString = "Server=" + sServer + ";Database= " + sDatabase + ";Trusted_Connection=yes";
    }
    else
    {
        // Create the connection string for a logged in user
        sConnString = "Server=" + sServer + ";Database= " + sDatabase + ";Uid=" + sUserName + ";Pwd=" + sPassword;
    }

    // Create a connection object, passing the connection string
    SqlConnection oConnection = new SqlConnection(sConnString);

    try
    {
        // Attempt to open the connection
        oConnection.Open();
    }
    catch (Exception oException)
    {
        // Handle exception here
    }

    return oConnection;
}