Since you're familiar with TortoiseSVN, you can use TortoiseGIT!
For TortoiseGIT, you need a prerequisite install of GitBASH - once installed, you can forget it's there (it's the GIT CLI).
Otherwise, you can just fork the repository on GitHub so that you have your own version and you can modify the files on the website.
The terms used between SVN and GIT are similar but different - an SVN Commit performs a Commit and a Push operation in one go, but with GIT, you have to Commit and then Push when ready.
Push is not a term used in SVN, since Commit encompasses it.
Pull is the GIT equivalent of an SVN Update and will pull updates from the remote repository.