Whatever shows in your task grid and Gantt chart is what prints. To make your printout smaller and easier to read, filter out tasks you don't need and zoom the timeline to the dates you want.
Filter by date
Double-click the Start or Finish column header.
A filter appears. Choose the date range you want to print.
Hide completed tasks
Go to View and untick Show Complete Tasks.
Zoom the timeline
Use Zoom In and Zoom Out in the toolbar, or View > Zoom In / Zoom Out, to change which dates fit on the printed calendar.
The space before the first task
The printed calendar always starts about an inch before your first task. This space can't be removed, but filtering and zooming as above keep it small relative to the rest of the print.