For starters, you need tables and relationships that support what you need to do. What you describe is a many to many relationship. An employee can be assigned to multiple classes and a class links to multiple employees. This requires a join table:
Employees::__pkEmployeeID = Registration::_fkEmployeeID
Classes::__pkClassID = Registration::_fkClassID
If this notation is something you are unfamiliar with and you need help understanding it, see this thread: Common Forum Relationship and Field Notations Explained
With this setup, a portal to registration can be placed on the Employees layout and used to sign that employee up for classes. A portal to Registration placed on the classes layout can also be used to sign up different employees for that one class.
Here's a demo file. It matches Events to Contacts, but if you picture contacts as your employees and events as your classes, it's a pretty good demo file that shows how this can be set up and several different layout designs that can be used to work with a many to many relationship.
If you are using FileMaker 12, open this file from the File menu and FileMaker will create a converted copy of it that you can open and examine using FileMaker 12.
This is a "just to get you started" post. Feel free to use Post A Answer to ask follow up questions.
Thank you! Being new to FMP, it'll take a little while to absorb this. I am aware of the many to many requirements, I'm just attempting to work out the best design for the user.
My thoughts are to have the students (contacts) list(portal) on the left side of the screen - top right a pick list(portal) to select the Class(event) to enroll the student in, and then another list (portal) on the right side - under the the Class (event) that shows students (contacts) that are already enrolled
Thanks again for you efforts on this.. it sure makes life much easier to be able to ask an expert!
Please see my demo file for a simpler layout design.
What you have in mind can work with some scripting and conditional formatting, but make sure you can get the simpler approach to work for you first.