I maintain the FileMaker Pro database for the advertising company that I work for. I am the only person using the database, so it is only set up on my machine. I don't know a lot about computer networks, but I need to have a few other people accessing the same database. What do we physically need for this?

Set the database to multi-user, install another license on another machine and open databases on your machine. You must have enabled required network protocol on both machines.

On the second machine you will connect the databases via HOST button. Sometimes on TCP/IP network you must specify host address e.g. 192.168.1.15.