There are a couple of ways:
1. I have a dress/costume in mind and I "match" some part of the doll for the look I want.
For example: I LOVE Doll of the World. But many of the "dolls" from the 80's and 90's use the big smiling, blank staring superstar mold and blond fluffy hair. This look is not "my taste". (And I do like many versions of the the Superstar Mold, but most of the DOTW are terrible IMHO) So I look at costume and over look and go from there. I try and decide what I think the skintone, the facemold and hair color and hair style. Then I look for a doll that has as many traits as possible in one package already.
2. I like part of the doll but hate another.
For example: I don't like uneven or "wonky" eyes on dolls. So I will just repaint the eyes to my liking.
3. I have a certain character/design in mind and I'm trying to recreate it in doll form.
For example: I loved the concept of Mattel's "Splash of Silver" Barbie, but I didn't like the face mold (or platinum label) that was used on the doll. So I created my own "Splash of Silver" out of a Silkstone doll.
4. The doll speaks to me. Somehow, someway my "inner eye" sees something different in the doll.
I know many other artists see or feel a character in the doll and bring it out. And I'm sure there are as many reasons and ways to choose a dolls as there are artists. (Go to ebay and search for OOAK dolls and see how many different types and style show up.)
My this project I choose Mattel's "Palm Beach Honey" as my base doll. She was last year's Barbie Fan Club's "Club Doll". (Meaning to had to belong to the online club to purchase this doll.) I waited and finally found a nude doll for sale, at a good price. I choose "Honey" for one simple reason: She inspired me. I don't like this dolls as a "full package". I think the way she was dressed and her face-up coloring is unfortunate. However I saw this doll redressed, and the ideas started flowing out of me. If I change "X" and "y" and add "z" then I might really like this doll. And ever since then I've been a little obsessed with getting this doll and trying out my ideas.
Here is a picture of Honey before:
You can see she has the "tan" skintone and long platinum blond hair. I find this combination very striking. In fact it is the main reason I choose this doll, instead of one of the others from the Palm Beach line. (The only line with the "tan" Skintone to date.) However that is about all I like about the doll. I find her make-up (or face-up) a bit odd. Her eye make-up is a mixture of aqua, charcoal and shiny pearl, that not only goes well above the eye, but below it. The pearl surrounds the charcoal on the bottom, giving the doll the appearance of dark circles. (I don't know about you, but I try to hind my dark circles, not accentuate them.) Her peach colored lips while pretty, don't really go with her other make-up . And when you add in the yellow of her original outfit these choices seem even more strange.
I don't have the original outfit from Mattel but I think this yellow swimsuit gives a decent picture of the overall look from the box.
Next I will discuss, how simple changes could have made this doll better.