First of all, I am NOT a real photographer so my advice is probably not going to be what a real photographer would say. :)
When I did the photo shoot with Taeya I knew I needed good lighting. Natural is usually best and since I didn't have the help of professional lights, I decided to set up my spot near a window. I didn't want direct sunlight on Taeya because then it would be too bright and would also have stronger shadows. I took the pictures in the morning next to a window where the light was coming in but wasn't direct. (We have lots of snow right now so it helped make the room brighter).
For the backdrop, I used a large, soft white blanket that Phil bought me for Christmas. I think anything can really work as a backdrop, it just needs to be big enough and the color that you want. I liked the softness of the blanket I chose because it showed up a little in the pictures but wasn't overwhelming. Even a solid sheet can work.
I took the pictures on our bed. In order to create something to hold up the backdrop, I actually put the bassinet on the back edge of the bed and draped the blanket over it. You want to leave some space (a couple of feet if possible) between the photo subject and the backdrop. It'll help make the backdrop stay in the background of the pictures and not be as visible in the pictures.
In the JC Penny's photo studio, I saw them use rolled up blankets underneath their drape to give Taeya something to hold her or prop her against. I rolled up a towel and just put it in a "U shape" under the blanket so that she wasn't laying flat on the bed. While I took pics, I moved her into different positions, in front of it, behind it, draped over the top etc.
For the setting on my camera, I chose the flower symbol for closeup pictures. This allows the camera to focus on her and again, not get as much detail in the background. I didn't use flash at all. I don't remember actually turning it off (although I may have) but the lighting was bright enough that I didn't need flash.
Then, I just took tons of pics! Don't be afraid to keep shooting because 9 out of 10 pictures won't be one of your favorites. I have many where Taeya was moving around or her hand was in front of her face etc. I just had a lot of fun and made it work for us. I'll try to re-set-up what I did later today so that you can see pictures for a better visualization. I did find the bassinet wasn't wide enough so I had a hard time getting the corners of my pictures to have the backdrop in them.
Hope this helps. Please post some pictures if you try this at home (and leave me a comment)! I want to see your results! Have fun!