Almost all spells and rituals start off with the simple words: "Cast a circle." Rarely, if ever, do they explain why, how, or what a circle is! Let's start off with the basics, then. A circle is not actually a circle. Rather, it is visualized as a sphere of energy, extending around you, above you, and below you. In some traditions, it is always a certain size; in eclectic traditions, it tends to be "as large as necessary". Whether the circle is nine feet, eleven feet, or surrounds your entire house depends on you, your needs, and your abilities. The reason we cast circles when working spells and performing rituals is threefold.

1) It holds energy in, keeping it from escaping until we wish to use it in our spell work or ritual. Think of the directed energy as water you are trying to heat to boiling point, and the circle as the pot. Without the pot, you wouldn't exactly be able to boil the water, would you? Without the circle, it becomes correspondingly harder to concentrate and direct the energy to where you want it to go.

2) It keeps things out. I'm not one of those Pagans convinced that the Door to the Abyss is open and all Gehenna is crawling over the Earth, but there are some very negative influences out there. Not only negative astral entities, which are usually built from human hatred and fear, but also the negative influences present in a house - mundane energy which doesn't co-exist well with magickal, and emotional residue left over from the people living there. If you just had a fight with your parents/roommate/significant other, you don't want the remnants of that energy surrounding you in circle when you're trying to concentrate on a positive goal.

3) It creates a sacred space and gate between worlds. The circle, when properly cast, acts as a gate between this world - what is sometimes called the material world - and the astral worlds, which are sometimes called the Dreamtime, and which may be considered parallel dimensions, different permutations of chance, or anything else that works for you. Why do we need the gate? Because certain things are more easily done in other worlds - or dimensions - than it is in ours. "Astral education" cannot be completed in the material world, due to the hammering influence of mundane energy - this holds down your Younger Self, and makes it nearly impossible to expand your mind past everyday constraints. Why do we need the sacred space? It creates a place where we can safely focus our minds on something other than the immediate world around us, without having to worry about outside influences. It allows us to experience Divinity much more immediately, without having to make an effort to recognize it.

Find a quiet spot where you won't be disturbed for at least ten minutes. Take your place there, sitting, kneeling, or whatever feels most comfortable to you. Comfort is very important when learning how to visualize any form of energy - if your leg is cramping or your head is hurting, you won't be able to concentrate on the desired result.
Are you comfortable? Fine. Now, ground and center. Let yourself relax.
Raise your power hand up in front of you and point your index finger straight out. Visualize blue light flowing into your hand - either from your heart, your brain, or from the ground itself. When you have that image firmly fixed in your mind's eye, let the light flow out in a beam straight ahead of your finger, as far out as you want the circle to go. When you have it at the correct length, move your hand in a clockwise circle above your head, slowly, visualizing that line of blue light forming a perfect circle around you. When your hand returns to its starting point, stop and "feel" the circle. Is the energy intact? Is it flowing strongly? If the answer is yes, then you may complete the circle. Drop your hand down quickly while visualizing the blue light spreading out from the bottom of the blue line, coming together on all sides to form a hemisphere. When it has closed beneath you, throw your hand back up above your head, visualizing blue light spreading out above you into a hemisphere that joins with the first. When it has closed above you, bring your hand back down and touch it to the ground.
To remove the circle, simply reverse the process, moving counter-clockwise and visualizing the energy draining back into your hand. It's a good idea not to take that energy into yourself; allow it to drain off fully into the ground, instead.
Note: This is not the only way to cast a circle. When you have enough practice with the basic process involved, you can change your method to whatever suits you best. Someone who identifies strongly with water might cast a circle that looks like a protective shell of waves closing over them. Several ceremonial rituals have specific circles that must be cast in order for the ritual to work to its full potential. Once you've gotten the basic circle, experiment with other visualizations and tools.