Thank you for your post.
After downloading FileMaker Go, it should appear in iTunes on the left side of the window under "Apps" in the Libraries section. Next, connect the iPhone to your Mac and select your iPhone under "Devices" on the left side of the window. On the right side, you will probably default to the Summary tab. Click the Apps tab and FileMaker Go should be listed. Check the Checkbox to "Sync Apps" and enter a check into the checkbox for FileMaker Go. In the bottom right corner, click "Sync". This will then move your FileMaker Go application to your iPhone.
Let me know if you need clarification for any of the above steps.