Where and how is the aperture placed inside a lens? How come the image is not affected (no obscuring) by something inside the lens literally blocking light?
The camera lens acts like a funnel in that it gathers light. The aperture is a mechanically operated, circular opening. Its job is to adjust the working diameter of the lens. The greater the lens diameter, the more light gathered. When the light is feeble, we set a large aperture diameter. When the vista is brilliantly lit, we set a tiny aperture diameter. Additionally, the diameter of the aperture is often used to cause different imaging effects. This is possible because the aperture diameter is intertwined with shutter speed and the sensitivity setting (ISO) of the camera.
Now to answer your question: You can draw an imaginary line from the subject to the lens. You can continue this line as it changes direction when it passes through the lens until it bumps into the light sensitive surface of the image sensor or film. Now that you have drawn this line, draw another from some other part of the vista. Now continue drawing. You will find that you must draw zillions of lines. In other words, you must draw lines from every point on the subject to the top of the lens, to the center of the lens, to the left side of the lens, to the right side of the lens. In other words, light from a single point on the subject hits everywhere on the lens. All these rays pass through and then play on the film or digital chip. If you interpose a circular aperture, you stop some of the light rays that hit the boundaries of the lens. But you do not stop the remainder. Those that get though project an image on the film or chip. However, you have cut down the volume of light that can get though, and the image dims as you close down aperture diameter.
The mechanical aperture can be inside the lens which consists of many glass lenses. The aperture can be placed before the lens, the aperture can be behind the lens. We place the aperture inside to protect the delicate thin metal blades, and because the position will effect optical performance.
Where and how is the aperture placed inside a lens?
Exactly where it is depends on the lens design, but somewhere in the middle is a reasonable approximation. A Comprehensive Guide to Camera Lens Design and Zeiss Nomenclature has a number of diagrams that show cutaway diagrams of different designs, and you can see that the aperture isn't always exactly in the middle, but it's usually close.
How come the image is not affected (no obscuring) by something inside the lens literally blocking light?
There's not just one ray of light entering the camera from any point in the scene -- there's a whole cone of light, with rays from that point to every point on the front element of the lens. The job of the optics is to get all that light to converge to a single point in the image on the sensor (or film). The aperture blocks some of that light, but it also lets some light pass through, so a complete image still forms. By blocking some of the light, though, the aperture reduces the amount of light that can be focussed at each point, and therefore reduces the brightness of the image.
The fundamental reason you don't see the iris itself is that there's no light to illuminate it's back side (and even if there were, it'd be way out of focus). And you don't see a big black ring around the edges of the image because, as discussed above, light from the image travels through the aperture at many angles, so it's still able to cover the entire sensor (and then some).
The aperture (the size of the diaphragm) DOES affect the quantity of light that reaches the focal plane. You may not notice this because the diaphragm remain full open until you actually take the photograph, diaphragm closes to the set position and shutter opens to let the light reach the focal plane (film or sensor, whatever)
Sometimes the borders of the image receive less light that the inner part, causing VIGNETTING.
Also, it affects the quality of the image that is formed in the focal plane, once it gets through the group of lenses.
As light has to travel different distances in the outer part than the inner part of the lens, it may happen that at certain big apertures (wide open, small f numbers), the rays don't focus on the same plane, producing what is called SPHERICAL ABERRATION.
When the aperture is small (big f numbers) DIFFRACTION may occur, lowering the quality of the image.
Depending on the size of the diaphragm, the portions of the image that stay apparently sharp (focused) varies, DEPTH OF FIELD.
Finally, the relative position of the diaphragm, its shape, etc also affect the image formed in the focal plane.
The aperture is fully open, regardless of your aperture setting, until the instant the shutter is released. The aperture diaphragm stops down to the desired aperture setting, then the shutter opens and closes, then the aperture diaphragm opens fully again.
If a camera has Depth of Field preview, all this does is prematurely stop the aperture down to the setting you have set, and you see the effect (including the darkening) through the viewfinder.