Commonly a circle needs to be drawn physically. This ensures that the focus of the person cutting it was steady enough to clearly demark the lines.
Cliche beliefs that circles keep out bad things and are barriers help people tap into conceptual momentum in case they don't do a good job.
The belief that circle are a cure all that keep you safe has built some serious power.
Hardcore Ritual Circle
If I was going to cut a circle hardcore I would actually take some cornnmeal and physically draw a circle. If I'm doing the ritual outside I will pour a little water on the ground in front of the cornmeal and then pour the cornmeal over the water. This way the cornmeal won't blow away in the wind. I can't tell you how annoyed I am when Movies/TV shows have the circle broken by a bit of wind because people didn't do some basic thinking ahead.
After I lay the cornmeal I will get out an Athame. Athames are ritual knives. I believe that any knife with a good point will work, but everything gets more focused toward a purpose the more it is used. Using the Athame to cut the circle at the edge of the boundary, I walk the circle once counterclockwise to release anything that might have been there before. Next I walk the circle clockwise 3 times focusing on the circle being cut deeper and deeper into reality.
Fast and Dirty Circle
My favorite way to cut a fast circle is to snap my fingers or clap my hands with power. This means I focus "energy" into my hand(s), which builds astral, and then I snap/clap while KNOWING that the energy is expanding out in a spherical wavefront pushing normal reality out of the way ahead of it. Depending on how much energy and how fast and far I push it the circle grows like a bubble filling up. There comes a point where the internal pressure is balanced by the outer pressure... AKA the wave front stops and forms an edge. Kind of like the debris/water line where a wave pushes into the shore.
Letting People into and out of a circle
The common way people do this is to literally cut a doorway or a slash in the circle and let people through and then close it when people get through. I've done this, but it gets annoying having to open and close a circle 30 times over the course of a ritual. I've tried more automated entry ways. First I'll create an entryway with actual stairs (remember, I tend to lower my circle into lower realities). Another favored image I use is a Vagina. Yes, a Vagina. I cut a slit and image it as a Vaginal opening allowing things we want to pass, while things we don't want to enter or exit stay where they are. If the idea of creating and walking through a huge Vagina bothers you, then another image to use could be walk in hanging refrigerator slats. A few rows of those are pretty effective too. The basic idea is a protected entryway that people can enter and exit through without screwing up the circle. If everyone will just stay inside the circle GREAT, but it's easier to learn these techniques than to have to fight to maintain your focus when you're annoyed at people entering and exiting the circle.
Circle cutting has a solid effect. You get 5 practiced mages in a room together to watch one cut a circle using will and the other four will be able to declare the boundries pretty darn accurately without discussing it on their own. In fact, those practiced mages will be able to tell you how strong and deep the circle is as well as what essential rules the circle has. I have yet to see mages consistantly be able to help draw a solid deep circle by sharing a ritual together. Everything I've seen so far tends to be "you do it and we'll watch." Most mages in a circle will help reinforce a barrier with barriers of their own. If the ritual declares the intents of the circle out loud you get a pretty cool shared effect from this. Kind of like having 15 different people help dig a hole. It's gonna be a lot bigger and deeper than if only one person digs that hole.
Closing the circle.
Additionally, if you leave a circle up, people will usually end up walking through the edges of the circle. When persons walk through the barriers of a circle without remembering that the barrier is actually a barrier, they weaken the thought power of the barrier actually being there until there is no barrier... merely a nice easy place to manifest if you're non-corporial. The persons walking through didn't "break" the circle. They merely changed the rules and "edges" of it. If you've drawn the circle it barrier aspect will stick around a lot longer, but it can still be weakened.
However, as you get better and better at magic there is more of a chance that one of these days you'll cut a circle and have it strong enough to stick around... Oh the havok you can cause.
Speaking of havok. For the vicious fun of it, try cutting circles around homes and businesses. You're basically sticking high-octane in the engine of their lives. If they are manifesting success and keeping their thoughts on it they will experience it much more quickly and "magically". If not... well... Maybe a fast failure is easier than a slow delayed one.
Cutting a circle and staying outside it