If they have a copy of Filemaker, you set the database to be shared.
Then forward 5003 port requests to the FMP server through the router.
There is an IP address that accesses your network from the internet.
Each computer on your network has a local IP address 192.168.x.x or 10.10.x.x typically.
This is found in your network settings depending on the OS.
Sorry, they don't have the program and I wasn't planning on giving them a copy. I was hoping they can simply type in an IP address and then log in? This way works fin for when we are in the same office and using the same router, but when she is a her home office she can't access the database. I'm not the most computer savvy, so if you can explain it in simple terms I would appreciate it. Thanks
If you use Instant Web Publishing, you can publish your database to the web and then other users can access it via a web browser.
You'll need much the same settings DavidAnders has already posted, plus more to set up IWP. There's some documentation on this that comes with FileMaker you can study up on. Be warned that not all FileMaker features are fully compatible with IWP, so you may have to make design adjustments to your database to properly support IWP.
IP Addresses can be Static (constant) or Dynamic (may change randomly)
You have a dynamic IP address now (http://whatismyipaddress.com)
You have a router that allows the 3 or 4 computers to share that IP address with the outside world.
If you have the database running on one of your computers with sharing turned on
A request for your database from outside your local network will go the router. The router is not running the database and the request will fail (with or without error message). If you set the router to forward the request for that port to the computer running the database, outside computers will be able to access the database.
you can tell your router to forward port requests for Filemaker to that computer.
If your Internet IP address is 188.8.131.52 and the local computers' addresses are
Computer #1 192.168.0.2 (sharing the filemaker database)
Computer #2 192.168.0.3
Computer #3 192.168.0.4
You tell the router to forward Filemaker port requests to Computer #1 192.168.0.2
FMP10 IWP Setup PDF
Testing your IWP setup.
If the database does not open, the IWP settings in Filemaker or the database are incorrect.
 At another computer on the same local network, open browser and enter http://hostlocalIPAddress:591/fmi/iwp
This should work if the first test works.
 At a computer on another network, open browser and enter http://184.108.40.206:591/fmi/iwp
If the first two worked and this does not, the portforwarding on the router or firewall settings are incorrect.