You take three cameras, run some tests with them, post the images but don't tell the audience which images come from which camera. You then ask said audience to vote on what they think the best images are.
This was done by digitalversus.com - it involved a Nikon D750, a Sony Alpha 77 II and the Samsung NX1 (using a pre-release firmware, so quality and performance are higher now than they were during this test).
There were approximately 1000 participants for the blind test, the test covers things like ISO performance, colour rendition, detail etc the usual suspects.
When people only had the image to go on (not brand prejudice, ego and other inefficient human traits) the results put the Samsung NX1 at the top. Link to original article is in the quote.
Last Tuesday, we asked you to give us your opinion about the picture quality on a pre-production model of the Samsung NX1 (firmware 0.36...), compared to a Sony Alpha 77 II and a Nikon D750. Let's break the suspense right now: against all expectations, you by far preferred the Samsung NX1, which came in first, well ahead of the D750. The Alpha 77 II finished last with three times fewer votes than the NX1. Let's go into detail...