In Business Intelligence Development Studio (BIDS), open the Solution Explorer by clicking View > Solution Explorer in the menu bar (Ctrl+Alt+L).
Click the "+" next to the Dimensions folder in the Solution Explorer.
Right click the dimension you wish to process.
Click Process in the context menu.
Alternately....
If you have the dimension open for editing in BIDS, under the "Dimension Structure" tab there is a process button in the toolbar.
It looks like a recycling icon (three arrows each tip pointing to the tail of the next arrow).