If you know Python, I would do it with Python and Flask web framework. If you don't want to use the web service, you can extract the html data using XPath. You right click inspect the element within Chrome and get the path of the html tag you want to access its data. After that you use Jinja2 included with Flask to create your webpage with the data in it.
I don't know Python but I will try, thanks for the suggestion. Any other ideas?
You can also work with the data received in the board, without using the website with the Dashboard. For this, you can use apache2 or NodeJS. You can install apache2 following the instructions in here. NodeJS is already available in the image.
There are a lot of examples in the Internet about this that you may find helpful:
Finally I've tried to go with Python and Flask and it seems to work with the REST API of the IoT Kit. I've been able to retrieve the information but for now only in the console, not in a website. It's a steep forward so I will continue with this approach. Thank you very much for your help.
That's great fernando!
By the way, you can look at the "requests" Python module (get it with pip). It will help you a lot with http requests and getting json data.
If you need help with Flask, I can give you some pointers.
Also, you can fork my repo on github : https://github.com/speccy88/Flask-Examples
They are Flask skeleton with jQuery mobile, Angular, winjs...
Good luck :)