C and C++ don't have a standard library for HTTP or even for socket connections. Over the years some portable libraries have been developed. The most widely used, as others have said, is libcurl.
Here is a list of alternatives to libcurl (coming from the libcurl's web site).
Also, for Linux, this is a simple HTTP client. You could implement your own simple HTTP GET client, but this won't work if there are authentication or redirects involved or if you need to work behind a proxy. For these cases you need a full-blown library like libcurl.
For source code with libcurl, this is the closest to what you want (Libcurl has many examples). Look at the main function. The html content will be copied to the buffer, after a successfully connection. Just replace parseHtml with your own function.