For your purposes, the only relevant interaction with the neutron is the strong interaction. (The neutron also participates in the electromagnetic interaction via its magnetic moment, and in gravity, and even in the weak nuclear interaction, but those can be safely ignored in this problem.)
Basically, when a neutron overlaps with another nucleus, there is a large interaction in which the neutron and the nucleus can trade energy and momentum (scattering) or in which the neutron can be absorbed by the nucleus. The absorption reactions are more probable for slow neutrons than for fast neutrons. In fact, once the neutron is too slow to excite any of the vibrational modes in the nucleus, the capture cross section becomes proportional to the neutron's "dwell time" near the nucleus. In the business this is called a "one over vee" (or $1/v$, where $v$ is velocity) cross section.
In the scattering interaction, the most likely final state is the so-called s-wave, which has no angular momentum and is spherically symmetric. For a neutron scattering from a heavy nucleus like plutonium, the center-of-momentum frame is not very different from the lab frame, so the scattered neutron has about a 50% chance of changing direction and going backwards --- but is unlikely to lose very much of its kinetic energy. For scattering off of a hydrogen nucleus, which has the same mass as the neutron, the neutron in the final state loses on average about half of its kinetic energy. You can figure this out using the rules for energy and momentum conservation that you learn in first-year physics.
A neutron "moderator," which slows neutrons down, is usually made of hydrogen or deuterium. Designing a mixture of materials that gives the neutron velocity distribution you want, while keeping the neutrons near your fissile material, is a complicated engineering problem. Doing this design in a weapon, where everything is also moving very rapidly, is even more complicated; the details are not public.