Having a firewall protects your computer from intruders, but it can also interfere with things you want to do. If it's blocking Skype, for example, you'll be unable to even sign in to your account, never mind chat, make calls or send files. Disabling your firewall every time you want to use Skype would needlessly complicate your life. Instead, configure it to let Skype through.
Ensure Skype is not running. If you're using Windows 8's default firewall, open it and click "Allow an App or Feature Through Windows Firewall," and then click "Change Settings." If prompted, enter the administrator password or confirm that you want to continue. Find the entry for Skype in the list, enable all three check boxes on the row for it, and then click "OK." If Skype doesn't appear in the list, click "Allow Another App," select Skype from the list, and then click "Add." If Skype doesn't appear in that list either, click "Browse," navigate to the folder where you installed Skype and double-click the program file. If you're using a different firewall, the procedure will likely be similar -- if you can't figure it out, check the manual or help files for more information.
To work correctly, Skype needs specific ports to be open. When you first install Skype, the program picks a port above 1024 at random and uses it to communicate. If that port is unavailable, Skype falls back on ports 80 and 443; if those, too, are unavailable, Skype simply won't work. To solve this, open the Skype options, select "Advanced" and click "Connection" to change the port used by Skype to a specific one, and then configure your firewall to allow Skype access to that port. In the default Windows 8 firewall, open the firewall, click "Advanced Settings | Inbound Rules | New Rule," and then follow the onscreen instructions.
If you're using a school network to get online, your firewall may not be at fault. The network is likely to have a firewall, and it may have been configured to block all access to exactly the ports Skype is trying to use. Try disabling your personal firewall altogether and connecting to Skype -- if it still doesn't work, the network you're using is likely to be at fault. In this case, you'll have to get in touch with your school's network administrator to know how to solve the issue.