There are two ways, without a reason, with a reason.
Saying no without a reason in some cases is the easiest method: you just say no and the conversation moves on. However, if people ask for a reason, it is more difficult, but even then you can say “you don’t want to say” and if they try to give you a hard time about it, step out of the situation and realize that this is just a short term event (see timescales) and it will pass and life will move on.
Saying no with a reason is generally the better way to handle the situation, if the reason is something that can be shared and you’re OK with sharing it. It is the better way because it makes the “no” feel less like a rejection and more like a factor of bad timing. If you don’t feel comfortable sharing the reason, or you can’t share it, then say that and people will understand–if they don’t understand and instead give you a hard time about it, either they’re joking or their serious, and either way see timescales above.
These same rules apply to How to say Goodbye: “I’m going to go now, bye!” Works fine. It clearly communicates that you’re leaving, so that you can leave: problem solved. ”I have to go _____” If you want to give a reason.
This post is part of AttemptedLiving’s Conversation Resources, a collection of articles on conversation.