This is following the advice of Sean Allred
step 1, make sure it actually failed to install: open up a terminal and type the command tex --version.
step 2, check the last few lines of the install log by typing tail -n 500 /var/log/install.log | less which will display the last 500 entries in the log
step 3, look for any error messages, for example mine was
PackageKit: Install Failed: Error Domain=PKInstallErrorDomain Code=110
"An error occurred while extracting files from the package
“MacTeX.pkg”." UserInfo=0x7fb765f67ec0
{NSUnderlyingError=0x7fb765f9ae80 "The operation couldn’t be
completed. cpio read error: Undefined error: 0",
NSURL=file://localhost/Users/username/Downloads/MacTeX.pkg#root.pkg,
PKInstallPackageIdentifier=org.tug.mactex.texlive2015,
NSLocalizedDescription=An error occurred while extracting files from
the package “MacTeX.pkg”
step 4, Google the error message. In the case of the above message, many users who downloaded MacTex saw this message when there downloaded files were corrupted during the download process. These problems can occur when MacTex is downloaded through the official website and sometimes even when using specific servers on this page. Some of the users experiencing this error message had success when doing the download from a different server on the above page (rather than the one closest to their physical location - note servers farther away may take more time to download from). I had to switch countries twice, but it finally worked. In addition, some users report issues using firefox or chrome (sometimes switching to safari yields a successful download). If all of the above have failed, most users who used github or torrent to download the files, instead of the official site, seemed to do so successfully without any of the files being corrupted.
step 5, if you can't figure out the meaning of the error message and no piece of the error message (note please search for small pieces of the error message as things like your directory structure, user name, and other system specific information will vary from user to user and may lead to no search results when these pieces of information are included) seems to be triggering a search result describing a similar problem to yours, you then should ask the relevant online community (or contact the support team at MacTex) describing the problem. Be sure to include the error message so future users with the same problem will then be able to see your thread.
tex --versiongive you on the terminal? The error sounds like it was reported by OSX, not the installer itself. – Sean Allred Jul 29 '15 at 04:21/var/log/install.logcontain anything useful? – Sean Allred Jul 29 '15 at 04:23tail -n 1000 /var/log/install.log | lesswill give you the last thousand entries in the log. – Sean Allred Jul 29 '15 at 04:25homebrew-cask. – Sean Allred Jul 29 '15 at 04:40