How does one integrate individual filemaker files? I have a contact management file, a task management file and event management file but I want them to work together to create one big database that works together.

Is this possible and how do I go about this?

You do that by creating relationships between the data elements and by passing control over by calling scripts in the other files.

 

I suggest you start here: http://www.filemaker.com/support/training/fts.html

The "Basics" edition is completely free and you will benefit a lot from it.