Hello. I missed a midterm today because I thought it was on Tuesday. What is the best way to explain this to the professor?

Please don't send that. When I say please, I mean it. There are too many things thematically that are wrong. It's overly apologetic. It's worse than saying you're sick. If the student sent that to me, I wouldn't buy one word of it. I never missed an exam because I forgot the date. How can you forget when you're being constantly reminded by not only the professor but also fellow students? If anything, I'd be honest. Tell them the truth with evidence if you have it. Some professors will give you another chance to take the exam.

No email, in person, no fake emotions, no fake apologies. Just say it as it is.

Walk over to their office right now. Leave a note in their box if they aren't there and explain the situation. I assume your exams are scheduled independent from your typical class times; say something like "went to confirm the room for tomorrow and noticed the date."

Additionally, send an email, not saying how good of a person you are for not lying...but apologizing for not attending as scheduled and asking for any possible leniency.

You aren't the first kid to miss a midterm...

Apologize over and over again, they might be lenient and they might not.

You should NOT e-mail the professor. Talk to him/her in person and hope for the best. Your odds are poor.

I think emailing is the best option professors can be Brutal so have a back up plan if you are rejected

Try to be slightly more formal and to the point.

Also, say why you had thought the midterm was at a later date.
I would add something like: "I understand that I should have been more organized with test dates and such, but ..."

I would also add something about meeting him/her in person to address the issue (since it may come across as lay to just write her an email).

no prof would be that lenient