Jason Whitehorn suggested the main tables. Just to expand on what he was saying with respect to how do you mark off the training etc?
Assuming you had some extra columns on your EmployeeTrainingRecords table to track when the training took place, when the training was completed etc.
CREATE TABLE EmployeeTrainingRecords
(
Id int IDENTITY (1,1) PRIMARY KEY,
EmployeeId int NOT NULL,
TrainingId int NOT NULL,
Started DateTime,
Completed DateTime,
CONSTRAINT [EmployeeTrainingRecords_Employee_FK] FOREIGN KEY (EmployeeId) REFERENCES Employee(Id),
CONSTRAINT [EmployeeTrainingRecords_TrainingId_FK] FOREIGN KEY (TrainingId) REFERENCES Training(Id),
);
You may prefer not to have an identity column on this many to many table and use a composite key (employeeId and trainingId). The reason I prefer an identity column and single Primary Key field however is that it is convenient when it comes to mapping an ORM layer which is abstracted with something like a repository pattern. You can have all your entities implement something like...
public interface IEntity<T>
{
<T> Id
}
This makes finding entities by an id from a repository easier as they all implement the same interface.
Training Records
With the training records table you can lookup all training records for a particular user. From this you will then know what training has been started, completed or not yet undertaken. Obviously any other data which belongs to a particular instance of a training session being undertaken by an employee you could also add here.
EDIT
You may even like to include information as to when the training is scheduled? So you might also have a Scheduled datetime column on that table. This would allow you to not only know what training an employee has been enrolled in, but when it should be taken and when they 'actually' took it (denoted by the started column) and when they completed it.
These sorts of details come down to your particular domain requirements though. Just a thought...
I like the comment posted by @Jason where he effectively said that your old schema (data your importing) should not affect or influence how you design your new model / schema. As suggested you can write a throw away conversion app for this. Looking at it from this perspective though will free up your design (and constraints) and allow you to come up with something more natural that better befits your problem or what you're trying to achieve. I don't know whether your old data is considered legacy data, but there's no reason to carry forth the design if you think you can improve on it.