Start by opening up a new Analysis Services XMLA Query and log into the Analysis Services instance. You can do this by selecting File -> New -> Analysis Services XMLA QueryIt will open up what looks to be a T-SQL window but it will only accept XML commands against the Analysis Services database. The following query will back up a single Analysis Services database without encryption or compression.
<DatabaseID>Insert SSAS Database name here</DatabaseID>
Insert your own values into the <DatabaseID >, <File>,<AllowOverwrite> fields and run the command. Once you have it working, you can schedule it in a SQL Agent Job just like any other backup job that you may have out there. In the job step, select a type of “SQL Server Analysis Services Command”A more in-depth reference be found here: http://msdn.microsoft.com/en-us/library/cc917611.aspx#XSLTsection124121120120