The best way to visualize this is to use a packet analyzer like Wireshark and follow the TCP stream. HTTP simply uses TCP to send a stream of data starting with a few lines of HTTP headers. Often this data is easy to read because it consists of HTML, CSS, or XML, but it can be any type of data that gets transfered over the internet (Executables, Images, Video, etc).
For a GET request, your computer requests a specific URL and the web server usually responds with a 200 status code and the the content of the webpage is sent directly after the HTTP response headers. This content is the same content you would see if you viewed the source of the webpage in your browser. The query string you mentioned is just part of the URL and gets included in the HTTP GET request header that your computer sends to the web server. Below is an example of an HTTP GET request to http://accel91.citrix.com:8000/OA_HTML/OALogout.jsp?menu=Y, followed by a 302 redirect response from the server. Some of the HTTP Headers are wrapped due to the size of the viewing window (these really only take one line each), and the 302 redirect includes a simple HTML webpage with a link to the redirected webpage (Most browsers will automatically redirect any 302 response to the URL listed in the Location header instead of displaying the HTML response):
For a POST request, you may still have a query string, but this is uncommon and does not have anything to do with the data that you are POSTing. Instead, the data is included directly after the HTTP headers that your browser sends to the server, similar to the 200 response that the web server uses to respond to a GET request. In the case of POSTing a simple web form this data is encoded using the same URL encoding that a query string uses, but if you are using a SOAP web service it could also be encoded using a multi-part MIME format and XML data.
For example here is what an HTTP POST to an XML based SOAP web service located at http://192.168.24.23:8090/msh looks like in Wireshark Follow TCP Stream:
