For your own PWS weather website, you'll need four things:
1) a automatic weather station that provides an output that can be read by weather software ( Davis VP/Vantage View, Ambient, Fine Offset, etc).
2) weather software that supports your weather station (Free: CumulusMX, weewx; Purchase: Weather-Display, Meteobridge, WeatherCat ) (there are other offerings too)
3) a system that can run the selected weather software 24/7 to process the data and keep your website updated.
4) a public website that supports FTP (or SFTP, SCP) to have the weather software upload weather data to.
You might find it useful to start with some free weather website templates -- each of the software listed above have templates available for use (free).
Hope this helps...