You mean how to distinguish the usage of ~요 and ~니다 right? Both of them are formal finish words of sentence. And we use them to older people, or someone you don't know very much. But "니다" is more formal. I think we don't use it much in everyday conversation. For coversation, "~요" seems more natural. But "~니다" is very well used for sentences in books, speaches, or business communication. For example, if you talk to your korean friends "blah blah 니다" it sounds strange and awkard, but it sounds natural if you use it in your business phone call or presentation. Hmm.. and in my personal opinion, if someone use "~요" in his/her business presentation too often, I would feel his/her opinion on that speech is a bit weak or girly. It is all about nuance matter.

Kate Lee explained the two clearly. But "-요" is actually an *informal* ending meant to imply "I'd like to get along with you."