If you are using QuarkXPress to create your design, you must save the pages out of Quark as EPS files, then open those in Illustrator. Make sure your page size in Quark is the same size as the postcard size you are ordering.
In Illustrator, select the fonts and create outlines, and save as an Illustrator EPS. If you get a message saying "One or more fonts could not be outlined because the printer font is missing", then that font will need to be changed to a font that does have printer files. This happens when either a screen font is present and a printer font is missing, or Menu-Styled fonts were used in Quark. Do not use the menu-style options in Quark. It may look good on screen, but if no corresponding printer font exists, your type will default to Courier.