First of all your printer must be able to print borderless. In general terms Photo printers will but others need a border so check your manual.
In Word when you paste in the picture you need to right click it and select format picture. On the layout tab select "behind text". You can now resize the picture using the "Handles" in each corner and centre of each edge. Check that you have set the margins of the document to the maximum in File>Page Set up. Then look in print preview to see what will be printed. (Is all of the original picture there for example. Post back if this doesn`t work with your version of Word details and the type of image. (jpg, tiff etc)