You do not need Filemaker server. You will need to setup port forwarding on your router to forward port 5003 to your ip address that is listed under Filemaker Network setting and you will also have to be sure port 5003 is open on your firewall.
www.ipchicken.com to get your ip address to your router assigned by your internet provider.
Then on your ipad use the ip address obtained from ipchicken with the port to access the files. xx.xx.xx.xx:5003
port 5003 is the recommend port to use by Filemaker but is not the required port.
Sharing a database , after you follow S Chamblee network setup, you must use one of your Filemakers as a HOST, in not using a FMP Server. You can have a maximum of 10 licensed copies share the DB, intra or inter net. 9 external users and you can Open remote on the HOST computer also making the total 10. Check Knowledge base for setting up a HOST computer.
Sharing DB files, by other methods, wont work unless it is "one at a time" and you block other users.
Thanks Chamblee, that worked perfect. It works great now.