If I have a module that I installed and its causing a conflict with another module, how do I trace it down to see which is causing the conflict? Let's say the error message doesnt' give any useful information in finding the culprit module. How would one go about find the module causing the issue?
You can use the debugging methods mentioned in the comments, especially ddebug_backtrace.
Another, more manual option, is, to disable other enabled modules one by one, until the error goes away. Once you know the culprit, search the issue queue of that module (and the new module) and/or use the debug statement (or drupal_debug from the devel module) to narrow down the problem.
Some pointers on how to debug: https://drupal.stackexchange.com/questions/545/how-do-i-debug-drupal How do I debug my Feeds import not importing a field
And then of course, you should look at the web-server logs (apache, etc). Another way to debug issues like that, when you get the white screen of death, is, to execute a drush command on the command line - like cc or something like that. Often, the error message gets printed to STDOUT.
My method was to edit the core set_message() function in the /includes folder and add in PHP's debug_backtrace() function in there to see the full output of where the module is causing the issue.
This way works for me since I don't have to have xdebug installed or have to go anywhere else. I think its the easiest way to do a backtrace from my point of view.
If there is a better more efficient way do let me know.