For Word to be able to print 4 pages to a sheet, it needs to have 4 pages. Unfortunately you can't simply print a single page 4 times on a sheet. The answer to copy and paste is correct. :-)
Also be aware that you have two sets of print settings and these often function independently.
First is the Word Print Settings. These give the most predictable results. Here you set the number of pages to be printed on a sheet.
Second is your Printer Properties. You can also set the number of pages per sheet in here. Leave this as 1 or you are also likely to get a border around the whole lot if your single pages have a border.
Now, the Printer Properties paper size defaults to you document page size. Change it to A4, or whatever actual paper size you are using and select OK. Note that this will only apply until you load the Printer Settings again, then it will default again. (at least on my version of Word!)
Finally select Print from Word!