I certainly wish he would teach me.
This implies under the circumstances the event "he wouldn't teach me" is likely true. Maybe he has refused to teach me; maybe the circumstances have led me to believe that he wouldn't agree to it. Or he hasn't agreed to teach me. "A: I wish he'd teach me. B: Oh, I am gonna go talk to him. I think he will!"
I certainly wish he taught me.
This implies what I wish were true but is actually not is "He teaches me." Namely, the event "He teaches me" is false. The speaker is talking about the present state of affairs. Maybe that event has yet to happen, or maybe it was possible in the past but is no more. For example, maybe Tom agreed to teach the speaker sometime in the past but appears to have changed his mind; or he may have mentioned it in passing in the past but has not demonstrated any trace of willingness to make good on his word recently.