What are multiple alleles how do they work?

This question is very open-ended and could be answered in many different ways.

Alleles are a symbolic way we represent traits in genetics, using alphabetic letters. For simplicity we often use two alleles to represent a single trait. For example, BB, Bb, or bb. A capital letter represents a dominant allele and a lowercase letter represents a recessive allele. In these cases, you have two alleles (which technically is multiple) representing a single trait.

The Law of Segregation says that of any organism (or organism's traits), half will be contributed to an offspring. The same goes in reverse: you have received half of your traits from each of your parents. For example, an organism with the alleles Bb for a particular trait can either contribute a "B" or a "b" to its offspring, not both. Other allele would come from the other trait. This phenomenon is shown any time you do a Punnett Square.

If by "multiple alleles" you mean more than two, then what you might mean is "multi-traits." For example, if "C" represented color of a flower and "T" represented if the plant had thorns and we wanted to know probabilities of these traits together, then we would combine them. If one parent plant was CcTT (let's say yellow and with thorns) and another was cctt (white with no thorns) we could create a 16-square Punnett Square to determine the probability of the traits together.

The easiest way to segregate each parent's traits is to combine them in every possible combination: first with first (CT), outside with outside (CT), inside with inside (cT), and second with last (cT). [This example is only the first parent. You would want to repeat with the second parent as well.]

If you are not talking about Mendelian probability and are meaning how do multiple alleles (genes) work together, then this gets more complicated and would need a more specific question with more context.