Currently, at least for the Fan Chart app and others that I've created, the best way to print them is to print them to a PDF file, and then subsequently print that PDF.
This may not work "out of the box" for all systems, but many Windows or Mac operating systems have a way of setting up a PDF file as a print option - and if you have that available, then do a regular print (CTRL + P or CMD+P on a Mac), which will open up the Print Dialog - choose the print to PDF printer option (or View as PDF), and save the file.
The top portion of the Tree Apps (where you enter the wikitree ID and choose an app) has been coded to NOT show up when you print, so what you SHOULD see is the meat of the app - the display that you want to print.
For the Fan Chart specifically, you may have to resize the chart so that it can fit on one "page" of the PDF (you may also be able to adjust the settings to capture it as well). I have designed the chart using vector graphics, so, it should resize well, and you should be able to send the file to a professional printer (Staples / Kinkos / etc) and have it printed on oversize paper and still come out looking okay.
Hope that helps!