One option would be to add a new link to the popup window that allows users to print the popup contents. You can add a new link next to the existing popup zoomTo link. Here's an jsfiddle that shows this:http://jsfiddle.net/drUvW/And here's info on how it works:
var printLink = dojo.create("a", {
"class": "action",
"innerHTML": "Print",
"href": "javascript:void(0);"
}, dojo.query(".actionList", map.infoWindow.domNode)[0] );
Next register a function that will be executed when the print link is clicked:
dojo.connect(printLink, "onclick", printPopupContents);
In the function you can get the selected feature then use the getContent method to get the info window contents for that feature.
function printPopupContents(){
var feature = map.infoWindow.getSelectedFeature();
var popupContent = feature.getContent();
//write contents to new page for printing
var newWindow = window.open("", "PopupContents");
console.log(popupContent);
newWindow.document.write(popupContent);
}