how does a genotype influence phenotype?
Because genotype is like the blueprints for the building, and phenotype is what the building looks like when you are done making it.
Genotype is the genetic makeup for an organism. Let's just talk about people.
Are your eyes blue? Is your hair black, red, blonde? Curly? Straight? These physical traits that we can all see are your phenotype (among many others...this is just a simple list).
These traits are controlled by genes in your DNA. My blue eyes are an inherited trait, part of my DNA - part of my genotype. The Phenotypic characteristic of this genotype is my sparkling blue eyes :)
So in this way, the genotype is like the plans or blueprints for a building, just like your DNA is the plans/blueprint for you. Your physical characteristics, those are your phenotype, but they are controlled by your genotype.
There are a lot of things we learn in life, though. These are not necessarily phenotype, though, because they are not linked to DNA. I teach chemistry in China. I'm from California. I speak English as a native language, whereas my students speak Chinese as a native language. These are not phenotypes that derive from genotypes (the ability to learn language is linked to our DNA, though). If I had been raised by Chinese speaking parents, my native language would be Chinese. So the things we learn in life are not phenotypes, but the ability to learn them is part of the phenotpye, since it is linked to genotype.