technically: open it in photoshop or illustrator, and save as an EPS. Realistically: it will never be a true EPS, as you would be saving a raster file as a vector file. So, it will lose resolution if you scale it, and it will not have selectable "parts" like a traditionally created EPS.
depends on how complex the graphic the is but you can find software to convert it to vector. Google "raster to vector" - I've tried a couple and the less complicated the image the better they work. You might be able to find someone on here who will convert it for you.
Save it as an eps in photoshop. But like markn26 said it will never be vectors unless you convert it. You could try the trace tool in illustrator, but if its a small gif image i doubt there is enough detail in it to do a good job. Your best bet would be to trace it by hand using the pen tool in illustrator
Bjam has it. I've never worked with Illustrator but it's gotta be similar to Inkscape and Flash. I use Flash more than Inkscape (more dummie friendly), and usually I import the raster (and I usually use a large ong version of the image), trace bitmap (setting options to 1 px, tight corners, etc), and then check it. If it's unacceptable, then I will use the pen tool and redraw it (I make another layer on top, then draw on that, still seeing my original underneath). When using Flash for this, I must select my new trace or drawing and convert to a symbol, delete the imported bitmap. Then export as eps 3.0. I found that not converting to symbol (basically saving the vector version as a sub-file) or leaving the bitmap meant I'd still get a raster inside the eps (just like when you save raster as .eps in PS like Mark said). I found all this out working with a printer company. Many versions of images were sent before everything was cool. I really need to get back to Inkscape and work with it more. : (