How are sovereign nations' troops committed to U.N., NATO or other international organizations?

I was just reading an article about the U.N.'s utter incompetence in preventing the genocide in Rwanda in the early '90s, and I got to wondering, how are sovereign nations' troops selected for U.N. or NATO missions? Are they drawn by lottery? Can soldiers opt out of serving under the U.N. or NATO commands in deference to their own countries' sovereignty?