One of the great advantages of digital imaging over traditional film processes is the ease of printing on a variety of alternative surfaces. With a printer that uses pigment-based inks, you can print photos on many substrates, including fabrics, art papers, napkins or anything that will absorb ink. Getting the image to look right, however, is trial and error. You will need to adjust your printer settings based on the absorbency of your napkin --- which will be high, considering that the fabric is designed to absorb --- as well as its fragility.
Check your printer software to see what sort of adjustments can be made. You will need to be able to adjust the volume of ink the printer outputs. If you can do this, go to Step 3. If not, go to the next step.
Download and install a RIP, or Raster Image Processor, for your printer. A RIP allows you to control where each drop of ink is placed and how much ink is placed. You will need this level of control when printing because you will have to adjust the ink volume based on the absorbency of your napkin.
Attach the napkin to a piece of photo paper for support. Because the napkin is made of such thin paper, it cannot be fed through the printer alone. Affix the napkin with photo corners if you want to preserve the whole thing. If you're willing to trim some of the edges, you can attach it with tape or glue. The latter method is much easier and more reliable, so it's advisable to go that route.
Measure the napkin and the paper to which it is mounted.
Open the image you wish to print in your photo editing program. Check the dimensions to confirm that it will fit on the napkin.
Load the paper with the napkin attached into the printer's feed tray.
Print the image with the "File>Print" command. Under "Paper Size," select the size of the paper the napkin is mounted to so the printer will know what size paper to expect. Position the image on the page so it will land on the napkin rather than the paper. Select whichever profile and paper type you wish, but remember what you use, because you will have to use the same combination each time for consistency.
Check the napkin to see how the image came out. Most likely it is a blurry, smeared mess. This means that you have to reduce the volume of ink the printer is using. If the image is barely visible, use more ink. If the napkin is ripped, you will either need to adjust the height of your printer head (if possible) or mount the napkin as tightly on the paper as you can.
Adjust these parameters as you test on various napkins. Getting the right amount of ink is trial and error, so be patient. At first, adjust the ink volume in small increments until you know what kind of effect it will have, then proceed according to your experience.
Save the settings that give you the perfect print so that they can be easily accessed for future projects. It is easier to forget things like that than you would expect. If you cannot save them, write them down and store the note in a safe place.