In the old days of teaching, grammar was the first step in the Trivium. One of the things emphasized was recognition of grammatical patterns. Teachers would have students diagram sentences, like this, in order to learn grammar and how language is built.
Now there are many ways to do this and it can even be helpful, especially in beginning Latin to diagram sentences and parse out the different parts of a sentence. The method I am most familiar with is the one taught by Fr. Reginald Foster in his Ossa Latinitatis Sola. In this method you are not so much diagramming as annotating the words in a sentence. Below I include the example he uses in his book.
Here is another example:
In short:
subjects underlined
objects dashed line
verbs dots under
parentheses or brackets for subordinate clauses
boxes around connectives
You can do do it anyway you want and any system will work. Students will of course need to know the different parts of speech but this is a powerful way to get them to see how sentences are built and with Latin word order being what it is