EPS is a file format based on the PostScript programming language. Many design applications can save files as EPS. EPS used to Illustrator's "native" format; now Illustrator actually saves its files, internally, as PDFs.
Forget EPS for the moment. If not with Illustrator, then with what application would you create the file? In other words, you must have some design software you use to create your files. What is it? Chances are it can save as EPS.
If you have no software at all, then you need to shop around based on what features you'll actually use. I'm not an artist, so can't advise. I know Illustrator's nearest competitor is Corel Draw.
tgreer
Made Her Cry
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You've entered the "raster/bitmap" vs. "vector" arena. Photoshop creates raster images. That is to say, pictures made out of little colored blocks. How many blocks? What size blocks? That's called "resolution". A high-res image will look great when you print it, but look terrible on screen. That's because a monitor can't display all those blocks. It will simply "throw away" what it can't display. The result is a jaggy mess. The opposite is true, as well. A lo-res image may look fine on screen, but terrible when printed.
The answer is to produce "vector" images. Vectors are mathematical constructs: description of lines, curves, and so on. That makes vector images smaller, but harder to digest. They have to interpreted, by a device, that will decide that a particular line or shape can be optimally drawn by, you guessed it, a particular set of rasters.
EPS files can contain either rasters, vectors, or any combination of both. So a Photoshop EPS will be rasterized, an Illustrator EPS (if the artwork is natively produced in Illustrator), will be vector. By "converting to outlines", they are asking you to "trace" your shapes to produce vectors. Illustrator can do that, so can Corel Draw.
In any case: you need to shop for a "vector drawing program".
tgreer
Made Her Cry
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If you are sending these files to a printer to have printed a work around is to create it at a higher resolution, at least 150 dpi (300 is better). The printer should then be able to use it.
rus
Junior Poster in Training
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