Search a Table for a Lack of Records
It is helpful if you post the table design, or at least what you will be joining on.  I created a sample that has 2 tables:

1) Student - Name (PK)

2) Training - Id (PK, Autonumber), Name, Class, Date

Create a relationship between Student.Name, Training.Name, enforce referential integrity.

There is a nice "Find Unmatched Records" query wizard in access that will get you going...  I used it as a base and came up with:

SELECT Student.Name
FROM Student 
  LEFT JOIN Training ON Student.[Name] = Training.[Name]
WHERE (((Training.Name) Is Null));


From here you can add additional logic in your where clause to whittle it down.

Edit : I missed the part about a specific class - this is probably closer to what you are after:

SELECT Student.Name
FROM Student 
where name not in (select name from training where class='your class here')