Nursing in a carrier is a great way to help meet your baby's needs when you either can't sit down, or if you want a little extra privacy.
My favorite is nursing in the Ergo. To do this, I lengthen the straps a bit, lowering the baby. Then I can manoever Baby onto the breast by moving my breast to his head level. I have found this to be an easy way to get Baby to sleep as well. For more privacy, just close the sleeping hood.
I never got the hang of how to nurse in the Moby. I think I managed once by squishing baby lower and squeezing my breast high enough to reach Baby's mouth. It looks like there is a way to do it by pretending it is a sling. Here is a video someone else did of how to nurse in a Moby Wrap using it more like a sling:
However you end up managing it, nursing while walking or in the grocery store is a fine feat worth attempting repeatedly to get it right! Good luck...