Your options are to either publish the database to the web, (For a small number of users, you can use Instant Web Publishing from a copy of filemaker pro.) or purchase a copy/seat for each client machine plus one more copy to host it or you can host it with filemaker server.
There are trade offs with each approach. Using IWP, saves you the cost of buying additional seats, but you give up some user interface capabilities and have a number of technical details you have to get configured correctly in order for IWP to work.
Why not both?