How do I split my view to show my script and beat board/index cards at the same time?

Go to View > Split and choose from the submenu:

This command divides the document window into two panels. To change what one or both panels show, click into a panel and from the View menu or the View icon in the Toolbar choose a script view, an Index Card view, Scene View or the Beat Board.

Split Vertically

Divides the document window into two side-by-side, upright panels:

Split Horizontally

Divides the document window into two panels, one on top of the other.

Unsplit Panels

1. Select the panel that will remain displayed;
2. Choose View > Unsplit Panels

- or –

2. Click the Split icon in the Toolbar and choose Unsplit Panels.

The panel that is not selected is hidden and the remaining panel expands to fill the document window. This command is disabled if only one panel is displayed. 

Swap Panels

Replaces the view of one panel with the other. For example, if a script is split vertically into two panels with the panel on the left set to Script View and the panel on the right set to Scene View, the Swap Panels command will place the left-hand panel into Scene View and the right-hand panel into Script View.