I'm just starting CD, but I did LL before. When I first started, I told friends and family only. I needed all the support I could get, after all! My friends and my husband were a little nervous at first, but once they saw that I could get through the first few weeks and I was OK, all that worry evaporated. They aren't worried at all now I'm on CD SS, in fact one of them was happier that I'm on CD (from LL) as she has a CDC as a client and has learned a lot about CD as a result.
Work was really difficult for me, mainly because the company I work for is very body beautiful and everyone there has a strong opinion on how everyone else in the office should lose weight. I'm by far the heaviest person in my office, and the majority of the other women are extremely thin and very competitive with each other over who's thinnest that week. I'm not exaggerating this a bit, btw - they mark down whatever they're competing over that particular month/week (waist/hip/arm/thigh measurements, weight) down in a communal calendar and make a big deal over who's ahead. On a site like this one, it makes sense, as we all have weight to lose... but from 4 women who are 5'9" and size six, it's a bit sick, really.
Anyway, I wasn't really interested in joining in the competition or getting any sort of focus on my weight loss from my coworkers, so I kept mostly schtum. I told one of my coworkers when I first started, mainly to ask her to let me know if the diet was affecting my moods or impacting on my job. I'm much more relaxed about it now. If someone comments on my weight loss and asks, I'll tell them. It's become more of an open secret since I switched to CD from LL, mainly because people want to know why. Since I switched over to CD, I've actually had one of the 5'9" size-sixers ask me if I could give her my unused LL packs, so she could fight the holiday flab.