You'll need to read the newspaper's rules to see what form(s) entries are permitted in. (i.e. have they got to be sent by snail mail or can they be scanned and sent by email).
However, assuming that there's not a link to a pdf version of the crossword (in which case, obviously, use that), you can simply capture the relevant part of the screen using the Windows Snipping Tool or Windows Snip & Sketch, save the image and then paste it into (say) a Microsoft Word document.
I use the Windows Snipping Tool, which was included in Windows 7 and 8 and (despite Microsoft promoting Windows Snip & Sketch) is still there in Windows 10. (It's under 'Windows Accessories'). Once you've opened it, click on 'New' and then drag a rectangle over the area you want to copy. Go to 'File > Save As' and save the image to any convenient location, ensuring that 'Save as type' is set to 'jpeg'. Then open a blank Word document (or similar), paste the image into that and print the resulting page.