See this MSDN article, for the section on backing up to a network share, e.g.:
BACKUP DATABASE YourDatabase
TO DISK = '\\SomeMachine\Backups\YourDatabase.Bak';
Backing Up to a File on a Network
Share For SQL Server to access a
remote disk file, the SQL Server
service account must have access to
the network share. This includes
having the permissions needed for
backup operations to write to the
network share and for restore
operations to read from it. The
availability of network drives and
permissions depends on the context is
which SQL Server service is running:
- To back up to a network drive when SQL
Server is running in a domain user
account, the shared drive must be
mapped as a network drive in the
session where SQL Server is running.
If you start Sqlservr.exe from command
line, SQL Server sees any network
drives you have mapped in your login
session.
- When you run Sqlservr.exe as
a service, SQL Server runs in a
separate session that has no relation
to your login session. The session in
which a service runs can have its own
mapped drives, although it usually
does not.
- You can connect with the
network service account by using the
computer account instead of a domain
user. To enable backups from specific
computers to a shared drive, grant
access to the computer accounts. As
long as the Sqlservr.exe process that
is writing the backup has access, it
is irrelevant whether the user sending
the BACKUP command has access.