Neutrons from DD fusion can be detected either at their initial energy in the MeV range as "fast" neutrons, or after their energy has been "moderated" by sharing it in successive collisions with light material -- particularly hydrogen. Fast neutrons can be detected by photomultiplier tubes viewing the proton recoil in plastic or liquid scintillation material. Slow neutrons (those that have lost almost all their kinetic energy and are in thermal equilibrium at room temperature) are conventionally detected by the charged particles produced when the neutron is captured with high probability in the nucleus of an atom of 10B (producing an alpha particle), or in a 3He nucleus, producing a recoil proton. A noble gas, 3He is used in the form of a proportional counter, while boron can be used either in the form of BF3 proportional counters or in the solid form, with the boron immersed in plastic or inorganic scintillator viewed by a photomultiplier.
Additionally, neutrons can be detected after moderation by their capture in some material of very high capture cross section (such as cadmium Cd), which produce several gamma rays that may, in turn, be detected by a photomultiplier viewing a scintillation detector. Similarly, neutrons moderated in water are almost entirely captured on the protons ("radiative capture"), giving rise to a deuteron plus a gamma ray with an energy of 2.2 MeV.
Finally, moderated neutrons may be captured in a trace element in the moderator (silver is a detector of choice) to produce a radioactive material that can be transported away from the experimental apparatus and counted separately with high efficiency at low background. The emitted radiation is typically a beta ray (negative electron), or a characteristic gamma ray following the beta decay. Of course, the world has enormous experience since the 1930's in detecting neutrons and detecting neutrons from the D+D fusion reaction.