Apache Web Server
Apache is normally the web server of choice for Linux. Here is the install link for Linux Apache. You may also use the install method for your particular Linux distribution.
You can test your web server by opening a web browser and entering http://localhost in the URL window. If everything is working, you will see a listing of your folders under your Apache root. Now find the ip address of your computer using ifconfig. Your ip address will show up as inet addr, probably on eth0. It will look something like 192.168.1.100 (your numbers will probably be different). Also, check to see if it works by entering http://your_ip_address in a web browser as you did with localhost. It should also show the folders under your Apache root. Write down this address, because you will need it later. If you have another computer on your network, open a web browser on the other computer and type the ip address of your web server in the URL window. If your web server is correctly installed, you will see the same file directory in the web browser of the other computer. If you are running a local firewall on your web server machine, you might need to allow HTTP or open port 80 on the firewall. Check with your firewall provider, or search the internet to see how to do this.