Apart setting mesh shading to smooth (which fakes roundness using normals, see https://docs.blender.org/manual/en/dev/modeling/meshes/editing/smoothing.html?highlight=smooth) you should probably learn about subdivision surface modifier (see https://docs.blender.org/manual/en/dev/modeling/modifiers/generate/subsurf.html), which creates new interpolated geometry in a non-destructive way (unless you apply the modifier, of course):
here you see a simple example: a simple basic cylinder, where you see the "prismatic approximation"
using the smooth shading you get something better (but it's just a smoothing faked, somehow):
instead you could use a subsurf modifier which creates the "missing geometry", depending on the subsurf level (here is 2)
since the subsurf "smooths" all, you get this weird result, but adding some "corrective" edge loop it gets better:
and you get this
which still has some lesser "prismatic approximation", but now the "smooth setting" works better
which is really quite smooth (and you can improve setting subsurf to 3, 4 or higher levels).
Of course your example image is more complex to "solve" because those are more complex object which only partly have cylindric sides.
You need to learn starting from simpler shapes, and experiment adding some edge loop as I did above, to keep some geometry "straight" and some "smooth" with control. The provided links have much info about this process, but believe me, you need to learn by yourself, failing many times, until you find the way.
You can also upload your file here http://blend-exchange.giantcowfilms.com/ and add the resulting link editing the question, paste it in the text. Then we can help with your specific file and setup.