Connected but won't work at home? I'm on my school laptop (MacBook Air) and it used to connect to my home Internet connection but suddenly it just..stopped. 

It says that I am connected. And I have full bars, my iPad and everyone else's computer is connected and are working, but my laptop won't. 

It's only my home internet too. It connects fine to my schools internet and all my friends internet. But not mine!!! Again I am fully connected but my browsers never load the home page (AND my Spotify won't connect but that's not that important).
From your question we can assume that you are connecting via WiFi and the WiFi icon on the menu bar is telling you that you are well connected.

The next step is to make sure you are getting a valid IP address. Open System Preferences > Network and click on the WiFi connection on the left. On he right it should now say something like "WiFi is connected to AccessPoint and has the IP address 192.168.1.21". There should also be a little green button next to the WiFi in the left hand pane.

If that is all ok then open "Terminal" and type "ping -c 2 www.google.com" and see if it then types 

PING www.google.com (74.125.237.179): 56 data bytes
64 bytes from 74.125.237.179: icmp_seq=0 ttl=58 time=27.140 ms
64 bytes from 74.125.237.179: icmp_seq=1 ttl=58 time=24.797 ms

--- www.google.com ping statistics ---
2 packets transmitted, 2 packets received, 0.0% packet loss
round-trip min/avg/max/stddev = 24.797/25.968/27.140/1.172 ms


you know the network appears to be working well and the problem might be your browser.