To give your PC a static IP, first find out its current IP address. (Network connections-->LAN-->Status). Then change the properties for the connection so that instead of being given an address/netmask/DNS server, you assign them manually. In fact you should be able simply to copy all of the entries from status; this will fix them.
Explanation: your computers are all on a subnet, and probably have IP addresses starting with 192.168.1. For example, the Linksys may be set up as 192.168.1.1 and then have a built in DHCP server that assigns IP addresses to the LAN, starting from (say) .10. Practice varies with each router. So your computer may have a current IP address of 192.168.1.11.
If you can get access to the router's interface (you'll need that later), you should be able to discover what IP addresses it allocates. It will usually only be a few (eg. from .10 to .20). If you can find that out, it is best to give your PC a number NOT in that range - e.g. 192.168.1.200.
You'll need to read the router's manual. It probably handles DNS requests for the LAN, so on your PC, enter the router's IP address as the DNS server (e.g. 192.168.1.1).
Whilst you're in the router, using the manual, set up port forwarding. All incoming requests on port 80 need to be forwarded to your PC's IP address (e.g. 192.168.1.200) on port 80. Make sure your PC's firewall allows incoming and outgoing connections on port 80. So long as you keep your installation of Apache up to date with the latest security patches, this is pretty safe.
Now your router has an external IP address - the one the rest of the world sees. To check to see if your web server is accessible to the outside world, first of all find out the router's current IP address (just use
http://www.whatismyip.com/) and then enter that address in your browser's address bar, with http:// in front. You should see your web server (unless your router specifically doesn't allow that kind of connection).
Report back!