What exactly are you trying to do?
Are you interested in programming and solving the equations yourself?
Are you running a lattice code and doing burnup calculations for fuel management? (what kind of reactor)
Or are you trying to run an ORIGEN type of calculation and looking at heat loads, doses, etc.?
Adding to queries from berkeman and rpp, what kind of resolution does one need? For example, one can calculate burnup for the entire core (core average burnup), on a group (e.g., batch) of fuel assemblies (batch average burnup), on individual assemblies (assembly average burnup), individual fuel rods (rod average burnup), the pellet (usually peak pellet, or pellet average), and down to the grain level (one needs a radial burnup profile, which is a function of pellet average burnup)
What does one mean by basics?
The level of detail depends on the goal of calculations, e.g., radiation shield design, or licensing level, or dose consequence in an accidental release, . . . . The level of detail also dictates the computational system, which can vary from a simple equation, such as
Burnup = (Thermal Power x Time)/(Mass of fuel), where the power could be in GW or MW, the time in seconds, hours, or days, and mass in kg or metric tonnes of U, HM (heavy metal), or UO2, or whatever form the fuel happens to be. Otherwise, we can describe in terms of percent of initial metal atoms that have been fissioned (fima).
In many countries, GWd/MTU or MWd/kgU, is a common unit for commercial fuel. Some countries, particular those with MOX fuel, may refer to GWd/MTHM or MWd/kgHM, where HM refers to U, Pu, Th, or whatever actinide is being used in the fuel material.