It's mentioned in the article that the highest energy ever recorded for a single particle was 320,000 PeV which is about 50 joules, i.e. the energy of a golf ball at 100 mph @_@
How they got so much energy in the first place is kind of an open question. Generally it involves magnetic fields and shock fronts, getting a little kick each time (but yes, you also have to avoid disintegrating the nucleus in the acceleration environment!)