How to tell somebody kindly that you observe Shabbat?

Coming from a family of non observants, and having just started to keep Shabbat at home I wonder how people navigate this.

If family members, friends, business partners or clients ask you to do something (go to an event or run an errand), are you explicit about the religious reasons why you cannot do it? Do you explain to them in detail what it entails? Or do you just blankly say that you cannot do it without giving a reason?

I am specifically struggling with clients that usually expected me to be available to do certain things on Saturday or Friday late afternoon, but I guess the question can be of a more broad interest.