If you're not already packaging your program with InnoSetup, I strongly recommend you switch to it, because it has facilities to make this sort of thing easier. You can specify any special situations, such as files that should not be updated if they already exist (i.e. if you have any internal configuration files or things like that), in the InnoSetup script.
Next, to allow the client machine to find out about new versions of your app, keep a very small file on your public web server that has the version number of the current release and the URL to the latest version's installer exe. For this file to be useful, whenever you release a newer version of your program you must update this file, as well as the version number in the InnoSetup script, and also some kind of APP_VERSION constant in your program.
Then, you'll need to handle these parts of the updater yourself:
- Detecting when a newer version is available by retrieving the current-version file from your web server over HTTP, and comparing the version number there to the app's own APP_VERSION. Make sure to do this query in a way that fails gracefully if the client machine doesn't have Internet access, and that doesn't block the GUI while it is doing the request (in case there's a network issue that forces the query to wait a long while for a timeout).
- If a newer version is available, asking the user if they want to update, and if they say yes downloading an updated installer to the TEMP directory. Depending on what GUI toolkit you are using, there are various mechanisms for displaying a progress dialog during the download; this is a good idea since the installer is likely to be at least an MB.
- Closing your app, running a special update script in the background, then starting up the app again.
The update script will wait for the original process to die completely (easiest way to do this is to pass in the original process's PID as a command line argument and have the update script send a query signal 0 to that process every second or so until it goes away.) It can then run the installer silently in the background, perhaps while displaying a "Please Wait..." dialog to the user. Once the installer is done and reports success in its return code, the updater can restart your program.
Depending on how big your app is, this is more wasteful of bandwidth than the method using git or another SCM. Every update with this approach would involve downloading the entire installer for the latest version of the app, whereas an SCM would only download the files that have changed. However, it has the advantage that it requires no special server facilities except a regular web server, and no special installation of the SCM client on the user's computer.
Plus, InnoSetup is just generally cool. :-)