What techniques/lenses/settings can be used to achieve really soft-looking photographs like this:
http://christieadamsphotography.com/blog/?p=2711
I've got an older Canon Rebel XT with a few relatively inexpensive lenses (50mm fixed, 28-135mm, and the kit lens).
I'm particularly interested in achieving the look where only the central features of the face are in focus and the other parts of the face and background are blurry.
You'll want a large aperture lens with a medium telephoto distance to replicate her photos. She lists her equipment in an interview and she appears to do a lot of her work with a 50mm f/1.4 and an 85mm f/1.8. Those are going to give you the look of the photographer you linked - in terms of the shallow depth of focus. But she is using a full frame camera, so you're going to have a tough time replicating her very shallow DoF shots on your cropped sensor Rebel.
If you're really digging her look and trying to replicate it - throw out any flash and artificial lighting - she's a natural light photographer. She bills herself as such and doesn't list any flash equipment among her equipment. She'll be using diffusing material or naturally diffuse light to create that soft light (soft light is the term for the long falloff off her shadows on the subjects). Think bed sheets, big windows with translucent blinds, cloudy days, shade from trees, etc. That soft look is a partly large aperture and partly soft light.
If she's doing Photoshop to make it softer (which it doesn't really look like she is much to me), you can try reducing clarity as @Steve Ross mentions or try one of the digital soft focus techniques here.
Baby photography (one of the big specialties of that particular photographer) is kind of a whole other world, so there's a bit more than just the right equipment. You'll need to be flexible, patient, have a plan - but be willing to adapt. Newborns have particularly splotchy skin so that's one reason you see alot of black and white there. Cute outfits and hats work to help 'deal' with some of their features that may not be quite in normal proportions yet.
Try lowering clarity in post processing and use a softbox or large diffusion screen (bed sheet would do) to soften the light.
The soft pictures in your link are mainly due to use of a fast lens (large aperture). This gives a shallow depth of field, which separates the subject from the background. Note that the face of the child is actually pretty sharp, and this is where the lens is focused at. Everything else is considered background and is intentionally blurred using that wide aperture.
For starters, the Canon EF-50mm F/1.8 lens is a very good and cheap option for such photography. A more expensive alternative which is a favorite among pros is the EF 70-200mm F/2.8L lens (but very expensive, though). There are a few lenses in between these two extremes that have large max aperture and good image quality.
EDIT: Just noticed that you already own one of the 50mm primes. Then, you already have all that's required to produce such soft, creamy portraits.
In addition to what's said above. Using a fast lens, you should try to manual focus on to the eyes. The eyes are what first draws a person into a portrait. The rest of the features don't have to be tack sharp, but your pictures will pop if the eyes are!
While the 50mm will give you a sharp focus, much of the creaminess comes in post production with photoshop. Try researching "photoshop actions". There are some many free ones too. I use MCP's "Magic Skin" action to help enhance the creaminess.
