The assumption is that you already have a cube that is built in SSAS and you would like to process this cube from sql server management studio
Connect to the sql server analysis services instance from the sql server management studio as shown below.
From the left hande side menu click on the plus beside Databases.
Right click on the cube that you would like to process as shown below.
The following dialog appears. Click on change settings if you need to and click on OK. Depending on the amount of data the processing takes a few minutes upto a few hours.