Hana prints just fine. Some things to know, though.
First, be sure that you are on a print-friendly page. Some pages are not meant to be printed (such as Gmail's mailbox view.) Some web-apps include their own print links. Use these to open a new window with the page in a printable format. Then hit ⌘-P or select Print from the File menu. Be sure to utilize the preview button on the Print dialog to make sure it looks like it will print well for you.
If you have any ideas on what print options should be included in Hana, please visit the Hana Contact Page and let us know what you think. We are working on better printing, but are interested in any innovative ideas to make it better.