Do I see the effect of aperture when looking through viewfinder?

I just bought a Nikon D3200 yesterday. I was looking through the view finder and adjusted aperture values. I thought I would see some difference, but I did not. Why don't I see that? Do I need to do some settings to see that effect before capturing a picture?

No - because most modern cameras meter & focus wide open (max aperture, smallest f number).

Some cameras have a function button, which you can allocate a function called aperture preview - pressing it then stops down the aperture to what you have selected (film SLR's usually had this feature). Not sure if the D3200 has it.

Deep Blue 2 is spot on, I would only add that the function is sometimes called "depth of field preview", and as you would imagine, if you've stopped down a long way, the image it produces is quite dark and often of very little use.

In this digital age, why not just pop off a test shot or two and zoom in on the viewfinder to check your focus/ DoF.

The D3200 does not offer DOF preview. Perhaps this is simply Nikon's acknowledgement that it doesn't work that well in the relatively small viewfinder of a DX sensor camera. I have it available on a few DX bodies and it's pretty much useless, so I don't use it. If it's critical, just take a test shot and review the image on the camera monitor.

In the early days of 35mm SLR cameras the photographer was forced to use what's known as stop-down metering. You composed the picture with the lens at its widest aperture (f1.8 or f1.4 or f2.0) and then, depending on the scene brightness or the amount of depth of field wanted, you stopped-down to the desired taking aperture (f5.6 or f8 or f11) and watched as the viewfinder got darker and darker, metered and then set the necessary aperture and shutter speed. Fortunately, in the early 1960s camera manufacturers invented meter coupling. This allowed the lens to be set at whatever taking aperture you wanted but the lens remained wide-open at its widest aperture so the viewfinder stayed bright and you could easily compose your picture and set aperture and shutter speed based on the camera's light meter. As you pressed the shutter release a mechanical linkage between camera and lens automatically stopped the lens down to the taking aperture.

Count your blessings that all modern cameras use meter coupled lenses. Although some cameras have what's called a "Depth of Field Preview" (DOFP) button which is used to manually stop the lens down to the taking aperture before you release the shutter, your D3200 lacks this feature. In my opinion that's no big deal because in all the years (over 41) that I've owned cameras with a DOFP button I probably haven't used it a dozen times. Even on a sunny day its almost impossible to see anything with a lens stopped down to f16 so I don't bother.

However, because I use a lot of wide-angle prime lenses I know what the DOF will be with a given lens at a given subject distance and aperture. You can learn about DOF here:
http://www.cambridgeincolour.com/...-field.htm

I can't add anything that has not already been said. I will just say I'm glad to see that *I* am not the only one who thinks the Depth of Field Preview button is a total waste. My first camera to have this was my old Minolta x700 and I found it worthless even in 1981. How can anyone judge depth of field on a almost totally black preview?

Best thing for you to do is simply learn from experience what various apertures will do for you with different focal length lenses.

Ther's a button for that in reflex cameras, when you look aperture is wide open

Normally when you look through the viewfinder it shows the view with the aperture wide open.
If you have a stop down button (or aperture preview) on the camera then pressing that will show the "effect" at the aperture you have set. Not all cameras have that function.