<p>I would like to know your experience when you need to take over somebody else's software project - more so when the original software developer has already resigned.</p>

The most success that we've had with that is to "wiki" everything. During the notice period ask the leaving developer to help you document everything in the team/company wiki and see if you can do code reviews with him/her and add comments to the code while doing the reviews that explain sections. Best for the "taking over" developer to write the comments in the code under the supervision of the leaver.