What relationships need to be done to have employee F & L names go into other tables when I enter on my main form?
You don't. In a database you use queries to link two tables. You only store information once in a single table.
Take a look at query all. There are four tables with information. Last name and first shows in all records, but it is only entered once in the DB.
I think you are over thinking these relationships. You only use a junction table when you have a Many to Many. I think that is only for your training. The other tables look like standard 1 to many. Any chance you can provide this db without any data or a couple made up records? It would be easier to fix than try to explain. Also can you explain in simple words the tables Program Information and Staff Wavered Sites and how they relate to an employee?
Do not use any special characters or spaces in a table or field name except for _. Do not use -/| &# etc.
For now do not worry about the many to many with training, but look at the example. Get rid of that junction table, you misunderstood what I tried to say. Besides training the other tables (with additional cleanup) are going to be 1 to many. So in those table the Employee_Number (not Employee_#) is the FK.
So the problem with waiting for an employee number is exactly what I cautioned about with natural keys. So If I was you i would have an auto number field called EmployeeID as your PK. In the other tables have EmployeeID_FK which relates back to the employeeID in the employee table. So in your other tables just rename EmployeeNum to EmployeeID_FK. The training table is the only exception because this is part of a many to many.
It looks like you are trying still to link PK to PK. This is almost never done. You link PK to FK. The PK is the one side the FK is the many Side. Employees have lots of courses. Each course belonging to that employee points back to the employee.