How can I change the way then calendar prints?
We print calendar screens using the layout "Calendar - no Side Menu". So you can make some changes there, but remember that this is also the layout you use in browse mode when you hide the calendar's side bar, so you probably won't want to make radical changes here.
If you do want a print layout that is radically different from the screen version, consider duplicating the "Calendar - no Side Menu" layout and making a version of it just for printing (adjust the script "Print Screen" to use your new layout instead of "Calendar - no Side Menu").
Remember that you can also print the Event List layout if you want to see more records than can show up on a month view (for example). Sorting this layout by Date reveals on of the subsummary parts which can make the layout a bit easier to read. Here again you might consider duplicating this layout and using it as the basis for your own layout used only for printing. Lengthening the body part, making the summary and description fields taller, and turning on sliding will let this printed list show more of an event's description than can show in the limited space allotted an event on the day, week, and month views.
But remember that the list view won't automatically "keep up" with the day, week, and month views so you'll need to build the found set to be printed by hand, or write scripts to find just the events you want to print.