If you're not familiar with networking, here is a basic tutorial, making the assumption that you are directly connecting your computer to the Smoothieboard.
Note: Since I'm "Low Karma" I can't post links, so you'll have to unobfuscate them. Sorry.
1. Connect your computer and Smoothieboard with an ethernet cable (also call often called cat5 cable)
2. Add / modify the networking config lines in the smoothieboard config file.
You can copy/paste the following or refer to the networking docs: smoothieware dot org/network
# network settings
network.enable true # enable the ethernet network services
network.webserver.enable true # enable the webserver
network.telnet.enable true # enable the telnet server
network.plan9.enable true # enable the plan9 network filesystem
network.ip_address 192.168.3.222 # the IP address
network.ip_mask 255.255.255.0 # the ip mask
network.ip_gateway 192.168.3.1 # the gateway address
3. Modify your computer's networking settings to match. Basically, you need to be on the same subnet but with a different IP address. Use the following if you're unsure:
IP Address: 192.168.3.1
Subnet Mask: 255.255.255.0
Gateway: leave blank
Info on setting up a static IP on Mac: www dot macinstruct dot com/node/550
Info for Windows: www dot howtogeek dot com/howto/19249/how-to-assign-a-static-ip-address-in-xp-vista-or-windows-7/
4. That should be all you need. Try accessing the Smoothieware interface in your browser at: 192.168.3.222
Good luck, let me know if that works.