You need a one-to-many table setup so you don't even need to enter repeating info.  You need to create normalized tables, which means each and every info is entered only once in the database -- no multiple entries of anything.  This is what Access is all about.  If you have to enter repetitious info, there is usually something wrong with the setup.  

The "one" side should be the class table, containing only info about classes -- class ID, class name, subject, teacher, etc.:

ClassID   ClassName   ClassLevel   Teacher
1         HU008       Remedial     Mr. T. C.
2         HU100       Freshman     Ms. J. D.


The "many" side should be a table containing the students of every class:

ClassID   LineNum   StudentName
1         1         J.A.
1         2         B.G.
1         3         S.D.
1         4         C.A.
1         5         W.K.
2         1         D.H.
2         2         H.A.
2         3         F.V.
2         4         J.A.

In the above, the first 5 students are in Class 1 (HU008), and the rest in Class 2.

Access is not Excel.  In Excel you can enter everything in one flat table, as you described.  But in Access, data have to stored in a highly structured manner with normalization and relationship.

Any reason why you wouldn't set this up as a Many-to-Many relationship?
My thinking is each class can have MANY students and each student can be in MANY classes.

Yes, many-to-many would be the next step.  Many-to-many is like having additional one-to-many relationships.  Another "one" table for storing student info would be needed.  A "one" table for teachers may be needed too, since each teacher can teach multiple classes.  In some cases, each class may have multiple teachers as well.