Jessi,
Please remove from your head any notion that this whole is some sort of magical mystery 
Anyone can make a usable pen. The rest depends on some practice, some very basic tooling and most importantly an eye for what
you like yourself.
If you are making pens for sale then you have to pander to the market to a certain extent, but when they are for yourself the world's your oyster
a. is this the sort of thing that can be done by anyone?
In most cases a reasonably priced small lathe will do the job fine. Carbatec, Bonnie Klein (below), Jet and many others make small lathes.
Tools - You should get by initially with a smallish spindle gouge (for roughing out) and a
very good quality skew chisel for finishing.
The oval skew needs a little more practice, but pays off big time

You will need a smallish (6" is fine) grinder and a couple of sharpening stones.
I have another post in here somewhere about using oil filters for faceplates for sharpening & such - have a poke about
BE CAREFUL about the woods you use however (there's a post about this too) -
a dust removal system is VERY necessary. These are not hugely expensive but remember how many sets of lungs you have

b. are there kits out there that I can purchase to do this?
As others have said - Yes.
c. does doing this require "turning" skills?
Generally, yes. The level of turning skill needed however is very basic, so pens are generally regarded as an excellent entry level project.
On the subject of women and turning - some of the finest turners in the world are women.
Check out
Betty Scarpino and
Bonnie KleinIf these ladies don't blow you away, nothing will

BTW - The threading jig shown on Bonnie's site is not particularly suited for cutting the sort of threads you would use on a pen. Most kits have these parts already threaded, so no big deal.
Regards,
Ruaidhrí
If you should decide to dive in,
give us a shout first before splashing out wads of cash - there are lots of things you will THINK you need, and won't actually need at all