There is no simple answer because it depends in the type of reactor, size, fuel lattice, enrichment (mean and distribution), neutron spectrum, power density, cycle length and batch size.
Type of reactor: LWR (PWR/VVER, BWR), SCWR, HWR, Graphite moderated, Liquid metal fast reactor, Breeder reactor. All use different enrichments, and some use moderators, while others do not.
Control Rods: Most PWRs have control rods withdrawn during operation, although some may use grey rods for power shaping and quick maneuvering (e.g., load following and frequency control). BWRs use control rods (control blades) during operation to control reactivity. In either case, the control rod system are designed to be able to shutdown the reactor with the highest worth rod(s) stuck out of the core.
PWR control rods usually contain Ag-In-Cd, but some may use B4C, Hf, Dy. BWR control rods contain B4C and Hf. One must be careful with Hf since it absorbs hydrogen and may swell thus compromising the ability to use the control rod.
BWRs use 'deep' and 'shallow' rods, i.e., the deep rods are more inserted than shallow rods. During the cycle, the deep and shallow rods are swapped to balance the exposure in different fuel assemblies. Also, different groups (sequences) of control rods are used to balance exposure in the different groups of assemblies in the core (Think of quadrant (and even octant) symmetry)
Booster Rods: In general commercial rods do not use 'booster' rods. It's not a term used in commercial plants. What does one mean by booster rod. Some research reactors, e.g., Halden, can use booster rods to enhance the local flux/power. In general, using systems that insert positive reactivity when inserted into the core is discouraged.
Boron: Soluble boron? PWRs use soluble boron buffered with LiOH (or KOH in VVERs) to control reactivity during the cycle. It may be roughly constant or slightly increasing early in the cycle, but then gradually (nearly linearly) decreasing throughout the cycle as enrichment is depleted. The concentration of B10 in the coolant depends on the fuel enrichment and excess reactivity in the core.
Moderator Level: PWRs have a constant moderator level, whereas BWRs, which experience boiling in the core, can adjust the liquid moderator level using flow control. Using flow control, BWRs can do 'spectral shift' in which more voiding takes place in the upper part of the core, and with a harder neutron spectrum, more Pu-239 is produced. Later during the cycle, the flow increased to reduce the voiding and the power is shifted upward to use the Pu-239. Cooler (lower power) assemblies have less voiding than higher power assemblies.
Xenon: Xe-135 is the most important isotope because of its high thermal neutron absorption coefficient. Xe-135 is a factor when reducing power or shutting down the reactor since as power is reduced, its concentration increases since the reduction in neutron flux changes the equilibrium.
Generally reactivity is gradually increased in order to prevent loss of control of a reactor. Negative reactivity may be abruptly added to the core, but in most applications, it too is done gradually, unless shutdown is the intent. Most changes are done with cents-worth of reactivity, and nothing approaching 1 dollar (Δ k = 0.0065 to 0.007, or one dollar of reactivity is equivalent to the effective delayed neutron fraction). Prompt criticality must be avioded in a reactor.
