This is easily done, you've zipped up your site to upload to a server and pushed to GitHub, you then get an error message like this:

remote: error: File Archive.zip is 214.15 MB; this exceeds GitHub's file size limit of 100.00 MB

...

 ! [remote rejected] master -> master (pre-receive hook declined)

error: failed to push some refs to ...

This helpful page from github has a solution. The steps are also below:

https://help.github.com

1. Open Terminal.

2. Change the current working directory to your local repository.

3. To remove the file, enter git rm --cached:

   git rm --cached giant_file
   # Stage our giant file for removal, but leave it on disk
   

4. Commit this change using --amend -CHEAD:

   git commit --amend -CHEAD
   # Amend the previous commit with your change
   # Simply making a new commit won't work, as you need
   # to remove the file from the unpushed history as well
   

5. Push your commits to GitHub:

   git push
   # Push our rewritten, smaller commit