If there's any contention at all, the state health agencies typically "determine need" by holding a
hearing which gives an opportunity for "the people in the community" to weigh in.
The way that works in practice is that at the hearing any hospitals in the surrounding area that care to do so will have someone show up to testify that it would hurt their business (and is "unneeded") to let a new place be built or expand near their area. The agency doesn't HAVE to take their word for it but in practice tends to do so - after the hearing, a committee that heard one voice FOR the new place and five or ten voices OPPOSED to it decides that "based on the weight of the testimony heard" there's no need for the new place. Unless a new lower-priced competitor can somehow generate the impression of a huge groundswell of support for the value of something new that hasn't even been built yet and thus can't sensibly be judged - in the face of really well-funded opposition - it never gets the chance to compete. So in practice, the status quo operations have a veto, even if the law doesn't explicitly say that.
Here's an example of an existing hospital requesting a need hearing so they can make their case to stop a potential competitor from getting some of their business:
http://wvuhealthcare.com/wvuh/Content/Media/News-Releases/20...
And here's an FAQ/description of the hearings:
http://www.doh.wa.gov/LicensesPermitsandCertificates/Facilit...
In most private sector businesses, if I think I can run you out of business by selling a lower priced product next door, I can just go ahead and DO that. There's no hearing at which you get to testify that there's insufficient NEED for my new restaurant/auto repair shop/what-have-you and thereby deny me a permit to build. Health care is special that way. In essence, hospitals belong to a government-maintained cartel.
UPDATE: in some states there do exist "objective standards" for what constitutes need...but it seems like what really matters is whether your Certificate Of Need application is UNCONTESTED (and might just sail right through committee) or is CONTESTED (so there's a hearing in which a bunch of lawyers challenge your right to compete - and probably find against you). Where there exist official standards determining how much supply is allowed in a given area, they tend look kind of like the documents here:
http://www.tennessee.gov/hsda/con_standards.shtml
Note that if you use those exact standards, starting a new hospital in order to undercut existing ones and drive them out of business due to your better/cheaper service is basically impossible. For instance, you can't start or expand a long-term care facility unless ALL the other facilities in your area have >85% annual bed utilization.