I see something strange like:
Now I'm not that CVS, SVN, etc. dude. When I open that in the browser it tells me that I did something wrong. So I bet I need some hacker-style tool? Some client?
(I mean... why not just provide a ZIP file? Isn't the world complex enough?)
Please Note: This is deprecated as of September 2013. See revised answer here.
Have a read through http://help.github.com/
To clone that repository via a URL like that: yes, you do need a client, and that client is Git. That will let you make changes, your own branches, merge back in sync with other developers, maintain your own source that you can easily keep up to date without downloading the whole thing each time and writing over your own changes etc. A ZIP file won't let you do that.
It is mostly meant for people who want to develop the source rather than people who just want to get the source one off and not make changes.
But it just so happens you can get a ZIP file as well:
Click on http://github.com/zoul/Finch/ and then click on the ZIP button just to the left of the repository URL field. See here: