SQLDMO.Application oApp = new SQLDMO.ApplicationClass();
SQLDMO.NameList oServerList = oApp.ListAvailableServers();
foreach(string strServerName in oServerList) {...}

// Connect using Integrated authentification
SQLDMO.SQLServer oSqlSrv = new SQLDMO.SQLServerClass();
oSqlSrv.LoginSecure = true;
oSqlSrv.Connect("ServerName", "", "");

// Connect using SQL Server authentification
SQLDMO.SQLServer oSqlSrv = new SQLDMO.SQLServerClass();
oSqlSrv.LoginSecure = false;
oSqlSrv.Connect("ServerName", "username", "password");
 

Disconnection is simple, but it is worth nothing the unusual casing of the DisConnect:

// Disconnect (note the capital C)
oSqlSrv.DisConnection();

Connect to the server as shown above to obtain a SQLDMO.SQLServer object, then:

SQLDMO.SQLServer oSqlSrv = ...
SQLDMO.Restore oRestore= new RSQLDMO.RestoreClass();
oRestore.Action = SQLDMO.SQLDMP_BACKUP_TYPE.SQLDMOBackup_Databases;
oRestore.Database = "NorthWind";
oRestore.Files = @"c:\backupfile.bak"; // C: = SQL Server's C:  drive, not client's C: drive

// Following required if we want feedback during the process
oRestore.PercentCompleteNotification = 10; // Message every 10%
oRestore.PercentComplete += new SQLDMO.BackupSink_PercentCompleteEventHandler(myPercentCompleteHandler);

// Start the backup
oBackup.SQLBackup(oSqlSrv);

...

public void myPercentCompleteHandler(string strMessage, int iPercent) {
    Console.WriteLine("{0}% Complete", iPercent.ToString());
}

Connect to the server as shown above to obtain a SQLDMO.SQLServer object, then:

SQLDMO.SQLServer oSqlSrv = ...
SQLDMO.Application oApp = new SQLDMO.BackupClass();
SQLDMO.Backup oBackup= new SQLDMO.SQLDMP_BACKUP_TYPE.SQLDMOBackup_Databases;
oBackup.Database = "NorthWind";
oBackup.Files = @"c:\backupfile.bak"; // C: = SQL Server's C:  drive, not client's C: drive

// Following not actually required
oBackup.MediaName = sqlBackup.Database + " " + DateTime.Now.ToString();
oBackup.BackupSetName = sqlBackup.Database + " set";
oBackup.BackupSetDescription = sqlBackup.Database + " etc.";

// Following required if we want feedback during the process
// Message every 10%
oBackup.PercentCompleteNotification = 10;
// See Restore example for implementation of myPercentCompleteHandler
oBackup.PercentComplete += new SQLDMO.BackupSink_PercentCompleteEventHandler(myPercentCompleteHandler);

// Start the backup
oBackup.SQLBackup(oSqlSrv);