I make no qualms to hide the fact that I think English grammar is really interesting, and I think my enthusiasm for it comes across in my teaching. (In fact, I'm the grammar teacher for my level at work... that is, I teach grammar to my own class in addition to two other classes).
Before I taught in Korea, and even after teaching there, I had no idea how to explain anything in regards to grammar. I had no idea about verb tenses, parts of speech, or any formal terms to explain the process and the practice of grammar. After I completed my TESL certification at the U of S, however, I realized halfway through my grammar and phonology class that I am actually one of those people who really get enthused about the underlying structures of the language.
I think that anyone who has struggled with learning a second language has probably sat through innumerable grammar classes with a teacher droning on about irregular verbs or some kind of impossible tense, but I take a different approach. I present the grammar structure we're studying, and have them take notes (so they can also practice their listening/note-taking skills), then I make them explain to each other (in partners) the concept I just taught them. I will then usually do a quick drill or worksheet to reinforce the concept before doing a class activity (role-play, discussion, game, etc) that requires more thought and creativity with the grammatical structure than a simple drill or worksheet.
When I first started teaching at my university, I had very little experience teaching grammar and not a lot of knowledge as to how to teach it. However, my amazing co-worker John, (also a former ESL teacher in Korea), created a handout for a presentation he did at a conference a while back which clearly explains all the verb tenses. Check it out here! (It won't make you tense, I promise).