This is the approach I used when when I moved everything to a new computer. Note that the backups can be stored on a secondary drive, an external drive, or some other computer on your local network depending on where you need to restore everything. Also note that you can use Windows Explorer (easy peasy) or a command-line tool like xcopy or robocopy depending on your comfort level. If you are using Windows Explorer, I recommend opening two instances. The first instance you use to browse around your local drive to find and copy folders to the clipboard. The second instance should be sitting in your backup folder (say D:\Backups or \\NAS\Backups) and is used to paste the folders from the clipboard.
Backup the Mod Organizer directory (and all its subdirectories) to a safe place. Using Windows Explorer, right click on the Mod Organizer folder, and select Copy. Alt-Tab to the second instance of Windows Explorer, right click, and select Paste. This copies the entire contents of Mod Organizer to the backup folder and may take a while depending on the number of files in the Downloads folder and the number of mods in the Mods folder.
Backup LOOT, TES5Edit, and Wrye Bash the same way.
You can back up all of the Skyrim folder (usually C:\Program Files (x86)\Steam\SteamApps\common\Skyrim) the same way or you can back up only the files you've added to the Skyrim folder (ENBoost, SKSE, etc.) depending on which method you are most comfortable with. The easiest and perhaps safest method is to back up the entire Skyrim folder. This way you know you haven't forgotten to copy something.
Finally, you'll need to backup the Skyrim data stored in C:\Users\<username>\My Games\Skyrim. This is where Skyrim stores the INI files it created when you first launched the game along with your all your saves.
Assuming you need to restore to a blank disk (or just wiped the disk and reinstalled Windows from scratch):
Install Steam and have Steam install Skyrim. When this finishes, run the Skyrim Launcher and select the appropriate video resolution and quality settings, and exit the Skyrim Launcher. This step is absolutely necessary so that it creates the required registry entries and the default INI files.
Restore Mod Organizer, LOOT, TES5Edit, and Wrye Bash -- use the same basic procedure to copy the folders from the backup folder into the destination folder (say C:\Games).
Restore the Skyrim folder (usually C:\Program Files (x86)\Steam\SteamApps\common\Skyrim) from the backup. Note that when I do this, I copy only those files in the backup folder that aren't already in the Skyrim folder so I don't overwrite any of the vanilla files.
Copy the Skyrim data files back into C:\Users\<username>\Documents\My Games\Skyrim.
Keep everything in your backup folder safely tucked away just in case you need to refer to them again.
Run Mod Organizer to verify your profiles still look good and then run Skyrim to make sure it works as before.