Most importantly, respond saying that you can not attend. It sounds obvious, but it’s easy to procrastinate and forget to send back the card saying that you want to decline the invitation. Forgetting to decline can lead to some confusion and an awkward phone call where you have to apologize and decline the invitation.
To explain why you declined, send a note or email to the person who invited you. You can also call, but that can get awkward. So, send a note politely explaining why you can not attend. Make it clear that you would love to attend, but you can not.
Explain why you can not attend. Be honest. If it is too expensive to fly to a wedding across the country, let the person who invited you know that. The person should understand that you just can’t spend $400 on plane tickets right now. If the wedding is local, apologize and state that you have a prior commitment or you can not attend for personal reasons. There is no need to elaborate. Simply offering that as an explanation is polite.
If you really do not want to go, simply say that you won’t be able to attend, you truly apologize and you wish those who invited you the best of luck. Even if the person or people who invited you don’t know why you aren’t attending, at least they will know that you put forth the effort to wish them the best and apologize that you can not attend.
Remember why you can’t attend, or why you said you can’t attend. You don’t want to accidentally mix up stories later, even if you were telling the truth. The goal here is to not hurt people’s feelings, not to hurt them inadvertently.