What is the relationship between genes, chromosomes, and DNA?

Let us start with DNA, and, to keep things more relatable, let us use human DNA.  Human DNA contains about 3 billion base pairs.  That is a really long code.  It would take nearly 100 years to read if you read one base pair per second for 24 hours per day.  To make things more manageable, the DNA is broken up into sections.  In humans, these sections are chromosomes, and humans have 46 total chromosomes.  That means a chromosome is simply a coiled up, long section of DNA.  Each chromosome contains thousands of genes.  A gene is a specific number of base pairs that codes for a trait. As a result, a gene can be defined as either a section of a chromosome, or a gene can be defined as a specific number of DNA base pairs.  
https://www2.le.ac.uk/projects/vgec/schoolsandcolleges/topics/dnageneschromosomes