SNIa are not quite standard candles, not good enough to by themselves make this measurement. However, experimentally it has been observed that their brightness correlates with how fast they brighten and then fade. This relationship, which is not well understood theoretically, makes it possible to measure how fast they brighten and fade and use this to know how bright they are. The difference between an accelerating and a decelerating universe is too small to be seen without this correction.
Second, what these guys did that no one had done before was to figure out how to find the supernovae. Up until then, the way it was generally done was that someone (generally an amateur astronomer) would notice a bright dot in some galaxy and report it. Then the professional astronomers would use large telescopes to observe it in detail and follow it as it brightened and faded. However, this only works for nearby galaxies that amateurs look at.
The problem is that professional telescopes are scheduled months in advance, but you of course can't know that there will be a SN in a few months time so you can apply for telescope time. What they did was sort of the opposite - by surveying a large number of galaxies with a smallish telescope they would be guaranteed to find a number of actual supernovae. They wouldn't know exactly where, of course, but with a large enough number of surveyed galaxies there would always be a few in some galaxies. They managed to convince the time allocation committees on the large telescopes that it was not a waste of telescope time to give them the time just based on the expectation that they would have something to look at. (I think this was the first time where telescope time was awarded to look at something that would happen in the future... ;-) With this method in place, the number of observed high-redshift supernovae skyrocketed.
SNIa are not quite standard candles, not good enough to by themselves make this measurement. However, experimentally it has been observed that their brightness correlates with how fast they brighten and then fade. This relationship, which is not well understood theoretically, makes it possible to measure how fast they brighten and fade and use this to know how bright they are. The difference between an accelerating and a decelerating universe is too small to be seen without this correction.
Second, what these guys did that no one had done before was to figure out how to find the supernovae. Up until then, the way it was generally done was that someone (generally an amateur astronomer) would notice a bright dot in some galaxy and report it. Then the professional astronomers would use large telescopes to observe it in detail and follow it as it brightened and faded. However, this only works for nearby galaxies that amateurs look at.
The problem is that professional telescopes are scheduled months in advance, but you of course can't know that there will be a SN in a few months time so you can apply for telescope time. What they did was sort of the opposite - by surveying a large number of galaxies with a smallish telescope they would be guaranteed to find a number of actual supernovae. They wouldn't know exactly where, of course, but with a large enough number of surveyed galaxies there would always be a few in some galaxies. They managed to convince the time allocation committees on the large telescopes that it was not a waste of telescope time to give them the time just based on the expectation that they would have something to look at. (I think this was the first time where telescope time was awarded to look at something that would happen in the future... ;-) With this method in place, the number of observed high-redshift supernovae skyrocketed.