Backup SQL Server to a Network Share

Solution 1:

Assuming that the SQL Server Service you're using has access to the network location, you can see a hands-on example of how to backup to a network share in either of the following, free, videos:
Backups with SQL Server Enterprise Manager
Backups with SQL Server Management Studio

This video also provides some information on other options and some caveats about backing up to network shares:
SQL Server Backup Best Practices

Solution 2:

In order to backup (as part of a schedule SQL Agent Job) to a network share you need to make sure the SQL Server service, and the SQL Server Agent service are running as a Domain account that has access to the destination folder.