You have a table in other database server, lets call in DB1 in ServerA. Then you created a SSAS Solution using BIDS, use DB1 as a data source, created a dimension and cube, and deployed the SSAS solution, for example to ServerB.
You want to make sure that your OLAP cube will have the same data with DB1.
You can create a SSIS package using BIDS, and then add Process Cube task to the package. Set the required parameters, and then deploy the package to your SSIS server. Create a job schedule to run the package, for example every 12 hour.