This is a basic videotutorial on how to use the Circle operator from the LoopTools Add-On, particularly to correctly create circles on curved surfaces, making it easy to perform extrusions both outward and inward on objects.
Video Transcript
Hello everyone! This is a basic videotutorial on how to use the Circle operator from the LoopTools Add-On, particularly to correctly create circles on curved surfaces, making it easy to perform extrusions both outward and inward on objects.
The tutorial was created using Blender 3.6, but the LoopTools Add-On comes with Blender from several versions of the software; however, by default, the Add-On is disabled, so first we need to find and activate it in the Add-Ons tab of the Preferences window.

After activation, the operators provided by LoopTools will be available by right-clicking on a mesh object in Edit Mode to open the contextual menu. Among the various operators, there is Circle. To show you an example, I'm using a cylinder that I'm intentionally scaling along its Z axis in Object Mode. I'm doing this operation because shortly I will show you a small issue and its solution.

I'm inserting cross cuts with Ring Cut to have some vertices to round off. It's important here that the faces are as square as possible to achieve a good result later on. You can proceed, for example, with just one Ring Cut, to be placed where you want to make the hole or the extrusion, and then perform the Beveling of that cut to obtain the other necessary cuts.

The Circle operator also works on a single vertex: indeed, it's possible to select a vertex, right-click, and choose Circle to see the surrounding vertices rounded off.

After performing this operation, however, we notice at least a couple of problems.

The first problem, quite evident, is that we haven't obtained a circle, but an oval, even though the faces that made up the geometry were quite square.
This problem is due to the fact that I resized the cylinder in Object mode without subsequently applying the scale transformations, so the Circle operator will create a non-uniform rounding.
To solve this problem, all we need to do is apply the scale transformations to the object before using LoopTools Circle. So, I undo the performed operations, switch to Object mode, apply the scale transformations with CTRL A and Apply Scale, then return to Edit Mode and use LoopTools Circle again, achieving the desired result this time.


The second problem is that rounded vertices introduce deformations that could get problematic later on, so it would be better to round a more limited set of vertices.
To solve this problem, once again, we undo the effect of LoopTools Circle, then select the faces within which we want to create the circle and press I, which is the shortcut for the Inset operator, in order to get a new set of faces within the selection.

Now, we can use LoopTools Circle again, this time on the newly obtained selection, to achieve a good rounding... but another problem arises: the newly obtained faces are flat, meaning they do not follow the curvature of the cylinder.

The solution to this problem is immediate... I mean that this operation needs to be performed immediately after using Circle: it's necessary to open the operator's menu and deselect the Flatten checkbox. LoopTools Circle is an operator, so the tab will be available immediately after applying the operator but will disappear after performing another operation, so Flatten needs to be deselected immediately.

Now, the geometry obtained can be extruded inward or outward from the object; moreover, it's possible to use Bevel on the rounded edge ring to create a smoother transition at the base of the extrusion.

Before closing this tutorial, a small observation: in an object like this one, all those cross cuts outside the area subjected to Inset are unnecessary and can be removed using some retopology techniques.

As you may have guessed, this operator works well for circles on simple surfaces: for holes or extrusions on more complex surfaces, it's better to resort to Shrinkwrap, but that's another topic... Let me know in the comments if you want me to make a tutorial on that tool, too.
For this tutorial, that's all! I hope it has been helpful to you! See you soon!