Ok, making a weather station these days is definitely not the hardest thing to do. As a matter of fact, there are tons of different sensors and libraries to implement one is a few hours. But what about storing the data?
Here is how you can connect the arduino with through the USB/Serial port to an Ububtu-running system and acquire these data with a Perl script. Having these data stored, you can come up with all sorts of different fancy ways to show reveal the weather history!
Check out this link for the details.