An introduction to brainwaves.

In Alpha Waves, Articles, Beta Waves, Delta Waves, Gamma Waves, Lambda Waves, Theta Waves by Lance Carter

What states we are normally in at different times?

Research shows that although one brainwave state may be dominant at any one time, the other brain states are present at all times; even though these may be present only at low levels. In other words; every brainwave state is actually a mixed state with one usually more prominent than others depending of
 the level of consciousness, activity and thought present.

That being said, let us look at them individually!
A brief look at the different types of brain waves and the states we are in.

The brain is an electrochemical organ.
Even though the electrical power in the brain is very limited, it does occur in measurable ways that are a character of the human brain. Electrical activity in the brain is measured in the form of brainwaves.

There are four main and well researched categories of brainwaves, and another four (depending on classification) that are less known or included in the other categories.
Brainwaves are measured in cycles per second or Hz (Hertz).
This is just a brief introduction. There are many benefits to each of these states.
The exact range of each wave is open to debate.

BETA:

The most common brainwave state is beta.
When the brain is aroused and actively engaged in mental activities, it generates Beta waves. These beta waves are the fastest of the four most common brainwaves.
The frequency of beta waves ranges from about 12 to 38Hz. Beta waves are characteristic of a strongly engaged mind. A person in active conversation or activity would be in beta.
Too much beta, especially in the mid to high range can lead to stress and anxiety without a break.
Too little, can lead to depression and inactivity.

ALPHA:

The next brainwave frequency is alpha. Where beta represented arousal, alpha represents non-arousal. Alpha brainwaves have a frequency range of about 8 to 12Hz.
A person who has finished a task and sits down to rest is often in an alpha state. A person who takes time out or practices meditation is usually in an alpha state. A walk in the garden or listening to music can create an alpha state.
Closing your eyes and taking a few slow deep breaths will quickly get most people into an alpha state also.
Alpha has been called the idling state; a bridge state between conscious and unconscious where you are ready to go either lower or higher depending on your next desired action.

THETA:

Theta brainwaves, are typically in the frequency range of between 4 and 8Hz.
A person who begins to daydream is often in a theta brainwave state.
Driving on a long straight road like a motorway or freeway, and realising that you can’t recall the last ten minutes, is often indicating a theta state – induced by the repetition of open road driving and helped by the rhythmic passing of road lines, poles and trees. Compare this to a country road where a beta state is required to drive safely.
Trance and hypnosis is mostly a theta state.
People in theta states often get good ideas during those periods. Runners can get into a mental state of relaxation that becomes theta and can have a flow of ideas. This can also happen in the shower or any time where tasks become so automatic that you can mentally disengage from them. The result of theta states is often free flow of ideas and thought without judgement.

DELTA:

Delta brainwaves typically range from about 0.5 to 4Hz. Typical of deep dreamless sleep. Body and mind recovery and growth occur in this deep brainwave state. Including the release of natural growth hormone. A lack of this type of brainwave pattern and deep sleep can lead to feeling tired even after sleeping for a long time. 
Typically, when we go to bed and close our eyes, our brainwaves will descend from beta, to alpha, to theta and then finally, when we fall asleep, into delta.
Humans sleep and dream in 90-minute cycles. Brainwave frequencies increase from delta into theta for active dreaming to take place. Usually, when this occurs there is rapid eye movement (REM), which is a sign of active dreaming.

The waking up process from a deep sleep involves brainwave frequencies increasing from delta to theta and then to alpha and finally, sometimes with the help of an alarm, into beta. If you hit the alarm snooze button, you will drop into alpha, or even into theta, or sometimes fall back to sleep in delta. It is possible on waking up, to stay in the theta state for ten minutes or so; which encourages a free flow of ideas and contemplation. This can be extremely productive with very meaningful and creative thinking.

The less known states:

GAMMA:

Gamma brainwaves are typically in the range of 38 to 100Hz. Although some would suggest that they are just higher beta waves.
These brain states are more common with creative inspiration, being in the flow, joy and compassion, increased awareness, and more exotic states such as lucid dreaming and Out of Body Experiences.
Long-time meditators in profoundly altered states and those in trance states often have gamma spikes appearing along with theta and delta.
This brainwave has a lot to still be learned about it as measuring technology improves. More and more these brainwaves are being seen and studies now with improved technology.

HYPERGAMMA and LAMBDA:

Both these brainwave states are more commonly included in the gamma range. The specific its of these states is a little unclear. Hypergamma is sometimes stated as between 100 and 200Hz. Lambda is even more rarely talked about and is sometimes stated as being 200Hz and above.
Little is known or measured in this range but feelings of empathy and connection and heightened awareness are reported to be present in these states in the few instances they have delta.

EPSILON:

Epsilon is most often included in delta for discussion.
When separated its frequency usually falls between 0.1 and 0.5Hz.
Very deep states of relaxation and detachment are possible for some; sleep is likely for most. At 0.5Hz for instance, there is one cycle (Neuronal firing) every two seconds. Very slow and hard to measure.