Whether you use an Ethernet shield or an ESP8266 to do wireless, the process of making a GET request to a server (Hey, server, run this script to use this data) is the same.
You need to develop the scripts on the server that take the data and shred it. Oh, wait, I meant store it somehow, so that you can access it, having a browser make a different request (Hey, server, run this script to show me what you've got).
So, what scripting languages do you know? What server software are you running? Apache, MySqQL and php were made to play together. Setting up a server, with Apache, running PHP scripts, saving data in a MySQL database is pretty easy. Hell, even I was able to do it.