Some universities allow faculty to nominate those chosen for honorary degrees. From what I understand, some even allow certain members of the graduating class and/or student council to nominate & vote. At other institutions, the senate, department heads, deans, president or chancellor may pick the candidates. Some institutions may have a nomination body and a voting body. I would think that it depends upon the size of the institution.
To find out for sure, check out websites for specific universities. Often times universities have focused areas of research or a campus wide research goal for which they have TONS of funding. On most occasions, honorary degrees are awarded to those who are conducting research in that field. They often award honorary degrees to those who are active in their communities as well.
Another common thing with honorary degrees: once an individual has been granted one other institutions will sometimes scramble to recognize that person as well. This is especially true if both institutions are located in the same area, or if they largely focus on the same research matters. People who make a difference on a global scale are often chosen as recipients of honorary degrees not only because they've made a difference, but because a university is, after all, still a business. If they give someone famous an honorary degree, you can bet it will be on the news. It will even get better coverage if other universities have also awarded the person with honorary degrees! Sometimes they look for a unique person to give an honorary degree to- because that will also get more coverage (for example, people from minority groups or from third world countries).
Each university has their own policy regarding nominations and different criterion, but they're all about creating a buzz. They may pick a First Nations community leader as a recipient in hoping that they will attract more students from that community. They also use honorary degrees as a way to network. If they want to meet their idol, they award them with an honorary degree so that person has to come and meet them to accept it (it is, after all, only polite, right?).
If you're curious about individual schools, you can look up the honorary degree recipients - they will often state why the person was given the degree. The key thing to remember is that they could come across anyone and find a reason to nominate them. They may see a firefighter on the news who saved the lives of people by rushing into a burning building. They attribute great courage to that person, so they nominate them to receive an honorary degree in emergency service operations. Their spouse, friend or neighbor may tell them an inspiring story which urges them to do more research on the person. Then that person ends up nominated! Yes, they have criterion, but it is flexible. They can word their statements for nomination in such a way that anyone would be fit for an honorable degree.