First you need connect your Arduino to your local network or the internet. You do not say what kind of Arduino you are using, but most cannot connect to a network by themselves.
How can this connection be made for your project? By an Ethernet cable? By WiFi network? By direct WiFi connection with a phone or tablet?
If an Ethernet cable is available, you can buy Ethernet shields that will fit onto an Uno or Mega. For other types of Arduino, you can also buy Ethernet modules that can be connected with a few wires.
If WiFi is available, a WiFi shield for Uno or Mega is an option. There are also WiFi modules available, and they are much cheaper, but they are more difficult to use than they seem. There is lots of bad advice on the internet about how to connect them to an Uno/Mega, that makes it seem easy. But there are problems with supplying power and translating the data signal voltages that this bad advice ignores.
Another WiFi option is to replace your Uno/Mega with a board that already has WiFi built-in, such as Wemos Mini or NodeMCU. This may be your best/easiest/cheapest option.
The next question is what this web page will look like, and what server will host it. Can you draw an example of how it might look, how the web page user can interact with it, how much history needs to be saved, will a database be required etc? Where will the page be able to be viewed? Options are: only by direct connection to the Arduino; anywhere on your local network; anywhere on the internet (in which case what about secrecy/security).