How does a gene cause a trait to occur?

A gene codes for a protein. So, a gene is transcribed into mRNA and taken to the ribosomes where it is translated into a protein. Whether this protein is a hormone, a structural protein, or whatever, it will go to where it is needed. Traits occur when the protein that the gene codes for is expressed.

A gene directs expression of a macromolecule (RNA or usually protein) that plays a role in some biochemical pathway(s). Either the gene product, acting in its pathway, affects development such that the trait appears (like a gene determining attached or unattached earlobes), or else it produces the trait in an ongoing fashion because it affects a biochemical pathway throughout life (like a gene that contributes to making pigment in hair giving hair color).

Gene expression is regulated at multiple levels and biochemical and developmental pathways can be complex, so the one gene - one trait relationship is often not straightforward.

the genes codes for a particular trait, and the coding is what tells the body how to express that trait.