Okay hm. I obviously have no idea what the magazine would actually prefer, but here's my advice as someone who has spent the last three years working on advertisement and article layout based on materials submitted by clients and contributors.
* My advice is that you don't at all resize the screenshot. If the magazine is expecting computer screenshots, they're going to be expecting exactly what a computer screenshot looks like - a 96 or 72 dpi image that is something like 1024x768 pixels. I wouldn't sweat it.
On top of that, in my experience, nothing is more annoying than getting an image from a client that has been messed with. In our graphics department if we get images that have been manipulated by the client ahead of time, we try as often as we can to get the original image, because the stuff the client did to the image is, 99% of the time, irreversable. For instance if you take a screenshot and blow it up to 300 DPI in Photoshop, what if the graphics guys didn't want that? They can't reduce it back to its original resolution without a huge quality hit to the image (note how
the blown up version of your avatar has all of that smoothing and blurring around the edges of the pixels? That would get massively compounded if they tried to reduce the image back to its original size; it wouldn't be smart enough to just scale back down to its original pixels, photoshop would try to reinterpret and interpolate when you sized it back down).
Plus, if the only change you're making in your end is a one-step photoshop operation to size the image to 300dpi, that's something the graphics guys can do themselves if they need it. You might just want to enclose a note in the email saying since its a computer screen capture you're including you obviously couldn't get a bigger one, but other than that I wouldn't worry about it. If they run into a problem, they'll let you know.
* If you run your computer screen at a higher resolution, you are effectively running at a higher dots per inch ratio (which is obvious if you think about it... pull out a ruler and count the pixels in one inch of your screen, then up the resolution a few notches and count again... clearly there are more dots per inch
).
So, if you're taking a screenshot of a game, for instance, or a flash movie (something that will scale up along with your screen res), just take the screenshots in the highest possible resolution your computer supports, and you'll be giving them more dots to work with. Don't worry about the DPI settings in Photoshop or anything - again, the graphics people at the magazine will know what to do with the images.
... That's all really. Basically, if you're trying to fix a technical problem with your image to match the specifications of the magazine yourself, chances are (no offense here) that the magazine's graphics people can do it better. Everyone would probably be happier if you just explained your problem but trusted them to do their jobs for you and fix it
Getting a grasp on the notion of dots per inch in print in relation to screen pixels is tough for a few minutes, but mainly all you have to think about in terms of DPI and screenshots is: it doesn't matter. Computers are pixel-based things. People know that computer screens are made up of dots; you see things like huge pixel based mouse arrows and extreme closeups of menus from office apps in advertising and magazine layout all the time. Nobody, including a layout person, would assume it was a print error or low quality image if they saw a 72 DPI screenshot of a computer in a magazine.
In terms of DPI in general, you have to remember that despite the fact that MacOS thinks to itself "i'm running at 72 dpi" and windows thinks "i'm running at 96" that totally doesn't matter, because the "DPI" you're running at changes with the size of your monitor and the resolution you're running it at. There's no correlation at all.
The only important thing to think about regarding DPI is the quality of the final print the magazine will be producing. Their printer clearly outputs to 300 DPI and they don't want artwork smaller than that (actually, realistically, they probably only output at 200 DPI but they want 300 DPI resolution art so they can print it 33% bigger without taking a quality hit). When they ask for 300 DPI art, they just want to make sure if people are submitting a photograph they will send a proper huge piece of artwork instead of a 320x200 pixel version they received from their mom via email or downloaded off Google images.
