The "why" has a few answers: Some cast a circle for protection, some to shift between the physical and etheric planes, some see the circle as a container used to store energy until the right moment to release that energy towards a certain goal.
Now, everyone casts a circle in his/her own manner. A circle casting can be very very elaborate, or very simple. We'll start simply:
The idea behind every basic circle is like a child setting up a tea party. Cleansing equals the set-up, calling in the deities/elementals/beings you wish to have present is like inviting the other children (or stuffed animals!) over, and the ritual is the actual party. The act of "casting the circle" part of casting the circle (if that makes any sense) is like setting a boundary between the attendees and the uninvited.
Setting up involves cleaning the area, physically, psychically, and energetically. Clean your practice area so you can move as you see fit. Cleansing with elements can be done by smudging with incense, carrying a candle around, asperging with blessed water, setting out stones around the boundary of where you plan to work...or a combination of any of the above. My method? I start in the northeast with my besom (broom) and walk counter-clockwise (widdershins) to "sweep out" negative energy first. Then I go back to the altar, take my incense (fire and air combined), bless it, then walk with it clockwise (deosil) to replenish the freshly-blessed air and fire energy. Back to the altar, consecrate and bless water (and add in 3 pinches of salt to make earth and water combined) so sprinkle that around clockwise to replenish the freshly-blessed water and earth energy.
I personally call in the elements before casting the circle, then cast, then invite the deities.
Calling the elements (watchtowers, elementals, etc) can be really simple: "I welcome the Air to my circle"...you can say this in your head while visualizing a breeze blowing or whatever makes you feel like "Air" is specifically present. Traditionally, people go to the East side of the circle to call the Air first, then South and Fire, then West and Water, then North and Earth. Some people do it differently...that's where reading and research is necessary to find out different methods and decide what works best for YOU. However, there's nothing wrong with trying it different a few times until it feels right...something might sound perfect when you read it, but how you feel when you actually do it is the key.
Casting the circle...you can use a tool (wand, athame, sword, staff, etc.) or just your finger. I begin in the northeast again, point to the ground with a tool or my finger, and visualize a beam of light flowing from the tip to the ground. I walk clockwise around the circle, say something simple like, "I cast this circle to create a boundary between the world of man and the realm of the divine" while visualizing that beam of light trailing behind, forming a wall or shell that the divine and energies I allow can get through, but nothing that I want to block out can cross. When I get to the starting point, I sometimes will bend down and tap the starting point like I'm connecting the two ends, and say something to the effect of, "My circle is now cast and whole!"
Now that everything's all set up, I invite my guests of honor: The God and Goddess. Sometimes I choose particular deities, but usually I just work with them as "God and Goddess." I light a candle and welcome them in. Don't demand that they join you ("I SUMMON you to join me!")...and don't be meek "Hi, um...if you can, can you please join me?'). Know they will come and greet them like you're greeting an expected guest at the door. "I welcome you to my circle and thank you for providing your energies to my work/ritual/celebration." Give them a vessel in which they can stay...a candle, a statue, a picture of each one, a stone representing them, etc. I usually welcome the Goddess first.
Now's time for your purpose of casting a circle...be it for meditation, a sabbat or esbat ritual, a spell...
After the main working, I hold a simple feast...some food and drink to replenish myself. A slice of bread and a glass of juice works, and it's suggested that you leave a small libation for the energies you were working with. Bless your juice, pour some into a bowl, and then drink. Bless your bread, break off a piece and put it into the bowl, and then eat. You can leave it somewhere or bury it when you're cleaning up afterwards...the idea is to visualize that those energies who are your guests are partaking of the food's energy (though maybe not the physical matter) before you just toss it in the garbage.
When I'm done, I thank the deities in the opposite order in which I welcomed them. Again, it's thanking them for coming...not saying "The party's over, so GET OUT." When you feel they have left (though they are always present) snuff the candles. So for example: "Thank you, Lord, for joining me in this ritual. Merry Meet, merry part, and merry meet again. (Wait a moment, then snuff God candle...then move on to Goddess candle.)
Then I cut the circle and either "absorb" the light back into my tool or finger (while walking counter-clockwise) or I "erase" it. Again, when done, I say something that completes the action, "By my hand, this circle is now erased and this area is returned to the realm of man."
Then, I wave goodbye to the elements...go to the North and thank Earth for coming, then West and Water, then South and Fire, then East and Air.
Finally, I return to my altar and make some sort of statement that the ritual is now complete. I usually do some kind of action like ring a bell or snuff out the last candle that marks the final moment...like a judge using his gavel and saying "Case closed."
Oh...and don't forget to clean up your area when you're done.
You can make this even more simple by sitting in one spot, visualizing a shell of energy growing up around you, and welcoming the elements and deities in your mind. Or you can be more elaborate with dancing, a script of flowery language and all statements in rhyme...whatever works for you.