As you will find with almost any field of science, you must start with the smallest components to truly understand how a process works. Therefore, to truly understand the anatomy of the brain, it is best to start with the tissues and cells of which it is composed.
Although there are many types of cells in the brain, neurons are the most basic cells that compose the brain and conduct brain functions. Anatomically, they can be divided into the dendrite (or cell body) and the axon (or long fiber that stretches out from the cell body). The axon is covered in insulation, similar to electrical wire insulation, known as myelin which allows for quick and proper transfer of electrical impulses along the neuron.
Impulses are passed along the axon to the terminus (or end) and there neurotransmitter chemicals are released in response to that impulse. Once released the neurotransmitters travel across a gap known as the synapse and are then absorbed by the dendrites of other neurons - thus passing impulses throughout the brain. These impulses can also pass along nerve fibers in the spinal column and out to the body.
From the outside, the living brain is a wrinkly grey organ with many different clefts and fissures. This grey tissue, known as grey matter, consists of the neuron dendrites. The axons, extending inward with their myelin sheath giving them a whitish color, create what is known as the white matter. The wrinkles are called gyri (ridges) and sulci (valleys) and allow the brain to have greater surface area in a smaller place. The gyri and suci are found on the outer layer of both the cerebrum and cerebellum.
The brain can be divided into a number of anatomical groupings. For our purposes, we'll divide it into the following categories: the limbic, the brain stem, the cerebellum and the cerebrum. The limbic system's core is found snaking through the interior base of the brain and contains the hypothalamus and hippocampus. There is some debate as to what other structures may be included. Generally, the limbic system is thought to control emotion and long term memory.
The brain stem is the most basic part of the brain and is responsible for autonomic bodily functions (or those actions your body takes without thought) - such as breathing, heart rate, blood pressure, gag reflex, swallowing, and sleeping/excitation. Additionally, the brain stem regulates the central nervous system and is the conduit for all messages between the body and the brain. The brain stem is located at the base of the brain and is continuous with the spinal cord. Structurally, the brain stem can be further divided into the medulla oblongata, pons, and midbrain.
Just over the brain stem, sits the cerebellum which is divided by a sulcus, forming two hemispheres. The cerebellum is primarily responsible for sensory perception and motor movement coordination. Recent studies have also suggested that the cerebellum is critical for certain cognitive functions such as comprehension of language and music.
The cerebrum is the large upper portion of the brain that is sometimes called the forebrain. The cerebrum is divided into two hemispheres (just like the cerebellum) which are identically comprised of four lobes (the frontal, parietal, temporal, and occipital). The corpus callosum sits between the two hemispheres and allows communication and coordination between them.
The frontal lobe of the cerebrum is where voluntary movement, reasoning, and much of our personality traits are processed. The parietal lobe sits behind the frontal lobe at the top of the brain and is primarily responsible for processing sensations. The temporal lobe is located to the back and side, near the temporal region of the skull. The temporal lobe is responsible for auditory processing (or hearing and comprehension). The occipital lobe sits at the back of the brain and is responsible for understanding visual stimulation.
Within the lobes there are centralized areas for their individual specializations, called cortexes. For instance, the motor cortex is in the frontal lobe and the somatosensory cortex is in the parietal lobe. Surrounding these cortexes there are generalized areas that are thought to store information and perform various thought and reasoning functions. These generalized areas are not fully understood.
The whole of the brain sits within cerebrospinal fluid, which helps to cushion the brain. This fluid is created and stored in sinus cavities within the brain, known as ventricles. There are four ventricles which are connected together. These ventricles are continuations of the spinal column and extend up into the frontal, occipital, and temporal lobes.
Lastly, remember certain electro-chemical reactions are required for the brain to properly function. Electrolytes, such as sodium, potassium, and calcium are responsible for the electrical activity of the neurons; which, in turn, release the neurotransmitter chemicals from the axon terminals. Serotonin, epinephrine, norepinephrine, and dopamine are among several types of neurotransmitters and are responsible for such reactions as mood alteration, excitation, calming, and pain impulses.
While not exhaustive, this article has given you a basic introduction into the anatomy of the brain. For further study, I suggest visiting these sites: