How to get support for modded installs
For help with stock versions of KSP, please check the Stock Support Forum
First, you should follow these troubleshooting steps
Following these steps resolves ~90% of all mod-related issues, which allows you to get back to playing and allows modders to spend more time focusing on the ~10% of issues that require their attention.
Make sure all your addons are up to date. Bugs get fixed all the time, and there's nothing worse for halting development of features / fixing of bugs in a mod than for a modder to be made to think a bug they have already fixed has returned. Please: make sure your mods are up-to-date.
Make sure you have all your addons installed correctly. Addons need to be installed exactly as they tell you to in their readme or opening post; if they don't say how, then follow this simple guide:
Find out if there is a GameData folder inside the archive. If there is one folder at the root of the archive, look inside it, and so forth.
If there is a GameData folder somewhere in the archive, take all the stuff inside the GameData folder in the archive and extract to (your KSP folder)/GameData/
If not, then you should probably extract all the stuff in the root of the archive to (your KSP folder)/GameData/ -- but note that some mods (like Universal Storage) have the folders you should extract into GameData inside a containing folder; in that case you should extract the folders inside the containing folder into GameData.
Check the stock help sticky and stock known issues sticky: you might be running up against a known issue in KSP itself. Self Help, Reporting Guide.
32bit KSP? Keep your memory usage low. The 32bit clients are limited to around 3.3GB of memory in use (it varies--reports show the limit is closer to, or even below, 3GB for Macs, whereas sometimes even 3.5GB survives on Windows). This has nothing to do with how much RAM you have installed; 32bit processes simply have a limited address space, and Unity does not handle allocation errors gracefully: it crashes to desktop. If you're running lots of mods, you're probably near the limit; try removing part-heavy mods and/or installing Active Texture Management in aggressive mode, which will reduce memory usage.
Check to see if the issue was already reported. Search the mod's thread (using the "search in thread" option) and search this forum (using the “search this forum" option) to see if the issue was already reported. If the mod has an issue tracker (see below), check to see if the issue was already reported there.
Reporting an Issue after you have followed the troubleshooting steps
To report an issue, please follow the following instructions. An issue report should contain the log, a set of reproduction steps, and be done in a clean environment with a list of the mod(s). If you don't follow these instructions, modders will ask you to do so before providing help, and that just slows everyone down.
Note that a number of mods maintain their own issue trackers. If a modder mentions (for example in the opening post for the mod, or the readme) that you should post your issue on their issue tracker (for example the issue tracker on Github) please do that rather than posting your issue here, but follow the same steps.
These are text files that the game spits out for debugging purposes as it runs; if something broke horribly in-game, there will be something in here about it. You should upload the entire log as a file (i.e. not to pastebin); you can use dropbox or an equivalent host to upload the file. Make sure the entire file gets uploaded; you may have to zip it first, as logs can be very long. Here is where you can find the log:
Windows: KSP_win\KSP_Data\output_log.txt (32bit) or KSP_win64\KSP_x64_Data\output_log.txt (64bit) or %USERPROFILE%\AppData\LocalLow\Squad\Kerbal Space Program\output_log.txt
Mac OS X: Open Console, on the left side of the window there is a menu that says 'files'. Scroll down the list and find the Unity drop down, under Unity there will be Player.log ( Files>~/Library/Logs>Unity>Player.log )
Linux: ~/.config/unity3d/Squad/Kerbal\ Space\ Program/Player.log
All files (logs, screenshots, saves and ship files) submitted for support requests must be uploaded to a file-sharing service and linked to in your support request.
NOTE: These logs are not the same as KSP.log, which lacks valuable data. Do not upload KSP.log; do upload output_log.txt / Player.log
The Reproduction Steps
These are essentially a recipe on how to cause the bug. If you don't include reproduction steps, the modder won't be able to reproduce the bug, and then can't fix it. The more detailed you make this, the better. Leave nothing out. Leaving out details can make bugs impossible to reproduce, and thus, impossible to fix. The gold standard for reproduction steps is an unedited video of you causing the bug.
If the issue stems from one mod, try to replicate it with only that mod and its hard dependencies in a clean KSP install. If the issue stems from the use of several different mods (for instance, Procedural Wings are still producing lift underneath a Procedural Fairing while FAR is installed) then get a clean install of KSP and install only the mods (and their dependencies, if applicable) in question.
This may seem like an extreme measure, but it ensures that only those mods (or the stock game) is to blame. Despite how complicated it may seem, it is actually quite simple to do (even for Steam users), as you can simply copy your install directory elsewhere as needed. It's especially useful since interaction bugs are some of the hardest to nail down; something that appears to be a bug in one mod might actually be caused by something else.
Regardless of how many mods are installed, you should include a list of all mods installed with their version numbers; a screenshot of your GameData directory is not sufficient, as it does not include version information and some directory structures may hide what mods are installed. Obviously, this is easier if you reproduce the issue with fewer mods.
Example Issue Reports
Note that this report has narrowed the problem down to the minimal number of mods (DRE Continued and its dependency, Module Manager) and the minimal craft necessary to cause the problem.