You basically cant backup your database to a shared resource as SQL server runs under a less priviliged account that does not have access to your shared resources. It does not matter if you execute a command (either manually or from the wizard) from an Administrator account and you have full access to the shared drives. SQL will call the backup process from its running account (Networkservice).
You could get around this in a couple of ways :
1. Change the user account running the sql service to an account that can access network shares. This however can be a security risk.
2. Backup to a local folder and have a seperate scheduled job move the backup file to the shared folder.
3. Buy a 3rd party backup software (Red Gate SQL Backup) that can backup to a shared drive.
Once you had open the management studio and connected to your server,
1) using management studio
2) select management, then select maintenance plan, right click to get maintenance wizard
3) name your Plan, then set the schedule by selecting the change button. (select your time/date you want the job to start)
4) select backup database (full) – as an example !!, OK
5) press next
verify the task and selct next
6) in database(s): select data database you want to backup
7) select crate backup file for every database, ( no need to place a check mark in creat a subdirectory box. Now, in folder path….you have to make sure to create a share folder in your other server where you will place the backup file.
8) path should look like this: \\youservername.domain.com(you have to place the name not ip. Then you domain)\yoursharefolder this should to the trick.
for example: \\myserver.google.com\sqlbackup