Here's how I learned 'em way back when:

Helping (or auxiliary) verbs:
be am is are was were been
have has had
do does did
may can must might
could would should shall will

Then the linking verbs--we didn't use the word copulative--sounded vaguely dirty:
be am is are was were been
become grow seem appear
taste smell sound look and feel

I always liked that order, ending as it does with the five senses.

I hasd a seventh-grade English teacher who considered sentence diagrams an art form. It was so drilled into us that I'm sure I could, given enough chalkboard space, do a compound-complex sentence with beaucoup prepositional and participial phrases, even now.