How Do Hormones And Neurotransmitters Influence The Brain And Behavior?

They are pretty much solely responsible for how we think, what we think, how we feel, what we feel, and what we do. Neurotransmitters are chemicals in the brain that essentially promote and allow the electrical impulses in our brains to travel. All of our neurological responses can be broken down to being simply electrical impulses. In order for an electrical charge to be carried across the brain, it has to travel through something called a synapse. Think of the electrical impulse like a train. Your neurons (the cells in your brain) are the tracks. And the synapses are the railroad switch. They let the pulse either continue on its original path, or divert it somewhere else. Neurotransmitters, among having other functions, are responsible for telling the synapses to activate, to let the pulse go through. If you have something like a mood disorder, or a psychiatric disorder, or if you are a drug addict, then the neurotransmitters will not perform their job correctly, which in turn leads to the electrical impulses not reaching their intended destination. Situations like these can lead to all sorts of problems; depression, anxiety, hearing voices, grandiose behavior, mood swings... Etc.

Neurotransmitters also effect the balance of hormones in your body. Hormones regulate things like fertility, growth, metabolism, the auto-immune system, and also can affect your behavior. Hormones greatly affect the reproductive organs and the limbic system (responsible for the "fight or flight" syndrome). These two respective systems play a large role in what your question is about, behavior. If too many hormones are produced in either of these systems, the resulting behaviors could be increased aggression/rage and increased anxiety, respectively. Too little, and the result could have more of a withdrawing, passive effect.