How do I snap/assemble two or more oddly shaped objects together?

Hi this might be a newbie question but I'm not sure how I can snap or assemble two or more objects that are oddly shaped together? Similar to how assembly works in CAD programs like AutoCAD or Solidworks, I have two objects and I want to assemble them.

The particular objects I'm dealing with are actually representative of one object cut in different pieces cross-sectionally. So I want snap the cross-sections of the object together. However, the edges are rounded but the cross section is approximately a circle.