Left: A mugshot sketch, which has nothing to do with making a screen print, but actually if I made a transparency of this it might be kind of fun to have it on a T-shirt. Pentel Brush Pen (the fine-tipped, dye based one), on pink stationery. Click on the image to view an enlargement.
In 2009 I walked readers through the conversion of a journal drawing into a screen print. I was using a Gocco Printer. These devices are no longer available, but the steps involved are still similar if you are working with regular silkscreening equipment or if you're using a Yudo (more on that in a moment).
So if you would like to have some fun printing your journal sketches on fabric or paper you might want to look (or look again if you've been reading since 2009) at these posts.
Next because I thought my first post was light on the explanation for why I did certain steps, and why I used an acetate overlay and how to use a toner photocopy, I wrote an additional post where I showed how I made an editioned set of prints from sketches made at the Bell Museum. (Since writing that post I have acquired another toner copier so I don't have to fuss around for some of the things I like to do with toner copies.)
Because Gocco Printers were phased out at this time I also wrote a short post on alternatives to the Gocco that I had recently heard of but not tried: specifically the Yudo. (I'll have more to say about the Yudo in a moment.)
The following year I wrote a post on Fabric Printing at the Textile Center, looking at the line quality possibilities using their Thermofax machine. Fabric artist Karen Wallach walked a group of the MCBA Visual Journal Collective members through the process. You can still rent time on the Thermofax at the Textile Center, but I don't know what the current details are, so please contact them directly for that information.
In other words
Divide each pixel dimension by the DPI as hglucky demonstrated.
High quality printing needs 300 DPI. You probably won't actually need that high a screen number.
Most desktops will print fine with 220 - 250 DPI.
Some very large format printers will print with as little as 38 DPI.
If you are printing at a service bureau ask them what DPI tolerances their machine can handle. A lot of people just say 300 but press them and ask what you can get away with.
For a desktop printer contact the customer service department of your printer brand and ask them the preferred dpi range for your model.
If you are using Kinkos, pray.