How will I know which aperture value to choose?

I'm using a Nikon FM10 and a Lumix DMC-GF2, and for both, while changing the aperture values, I don't see a change in the DoF when looking through the viewfinder.

Is the only to get the right shot is too try out different values and look at the developed pictures?

Both of your cameras have a feature called meter-coupled. What this means is that regardless of the aperture you choose - f/16, f/11, f/32, etc. - the lens remains wide-open at its maximum aperture - f/1.8, f/2.0, or whatever it may be - until you press the shutter release. Circuitry between the camera and lens (mechanical or electrical) "tells" the camera's light meter what taking aperture you've chosen (f/16, f/11 etc.) so the meter meters the scene at that aperture.

Your Nikon FM 10 has a depth of field preview button which you can use to manually stop-down the lens from wide-open to the taking aperture you selected.

The more you learn about Depth of Field (DOF) the better your results will be.

http://www.cambridgeincolour.com/...-field.htm

http://www.dofmaster.com/dofjs.html

You won't see the DoF when looking through the viewfinder normally.

You'd need to find the DoF preview button, if either of these two cameras have that function. Try reading the instruction manual, it should tell you if the camera has one.

The picture you see while adjusting the camera is normally through the wide open aperture and will not change. It only closes to the chosen aperture when you click the shutter.
If your camera has a Depth of Field Preview button, it will close the aperture while you compose the shot and you can see the DoF.
Look in the User Manuals.

According to the specs, the Panny has an electronic viewfinder which means it's not going to show you what's happening through the lens.
http://www.dpreview.com/...icDMCGF2/2
The Nikon viewfinder is described as a "fixed eye-level pentaprism" which also isn't "through the lens". The Nikon is supposed to have a Depth of Field preview so it's time to pull out the camera's user manual and go exploring.

Depth of Field is one of those areas of picture making were experience matters. Once you get experienced with your cameras, you'll be able to mentally calculate the aperture setting based on the "thickness" of the main subject and then hedge your bet (guarantee your guess) by taking shots a step above and a step below the setting you guessed was the right one.