By locally I assume that you mean your local desk and that your co-workers are on the same campus. To answer your question more specifically, we would need to know what your operating system is. However, your co-workers must be able to access the website through their IP address, as long as the network administrators have not blocked it in any way.
For example, if your IP address is 10.1.2.3, your co-workers should be able to see it through http://10.1.2.3. In MS Windows, you can go to the command line and type "ipconfig" and it will give you your IP address. I'm sure there is an equivalent command in your specific operating system.