None of it is easy. I haven't read this particular paper, but I have worked on similar experiments. First, you have to create muons and then isolate them in the particle beam and this costs quite some money (typically fire accelerated protons at a target and allow the pions and other decay products to be dumped in some dumb absorber that the muons pass through). Then you have to capture the muons into orbits around protons that come from hydrogen that needs to be disassociated and ionised. Then you have to pulse the hydrogen with a laser and excite the muon into a new energy state and accurately measure the energy of the photons that come off in the decay. You almost certainly need subnanosecond accuracy in your timing at this point. Of course, you can never be absolutely certain what you're measuring in any particular event so you sum over millions of events and average. And you have to simulate the whole thing (typically using a C++ framework called GEANT running on massive processor farms analysed with a horror-show of an analysis toolkit called ROOT) to see what could go wrong and determine the possible sources of error and uncertainty in your measurement.

To get the money to do this, you have to apply for government grants that may take up to a year to get approved. And no government wants to fund it so you need an 'in' with the lab, because they'll be the ones that sponsor your application for it to have a chance of success, and you'll need to know people from a whole load of other countries to collaborate with and prove your bona fides. And the people writing all these grant applications and doing most of the middle management are distracted by teaching literally hundreds of students every week during term time, so they can't even work full-time on it.

There are other experimental ways of doing this (e.g. measure correlated form factors and parton distribution functions from elastic scattering and extrapolate to zero momentum transfer), but they're all harder. They'll probably be done within the next 30 years. Probably. This particular effort is likely the work of 30-50 PhDs working for five or more years (at 50% of the salary they'd earn working for commercial companies), discounting any of the commercially available technology like electronics developed by CAEN or detector components developed by the likes of ElJen or Hamamatsu. And I would be surprised if they didn't mint another 10-15 PhDs during the effort. And I haven't covered the highly trained technicians and electronic engineers that are usually needed to build a lot of the custom experimental equipment.