First lesson: Tag questions

First of all, what is a "tag question"?

A tag question is a special construction in English. It is a statement followed by a mini-question. The whole sentence is a "tag question", and the mini-question at the end is called a "question tag".

Purpose

We use tag questions at the end of statements to ask for confirmation. They mean something like: "Am I right?" or "Do you agree?" They are very common in English.

Basic structure

Positive statement, negative tag

Snow is white, isn't it?

Negative statement, positive tag

You don't like me, do you?

Affirmative statements with the verb "to be"

It's a beautiful day, isn't it? 
Martha is angry, isn't she? 
You are really tired, aren't you? 
They're very nice people, aren't they? 
You are coming tomorrow, aren't you? 
Pedro's flying now, isn't he? 

There's only one exception to this rule: 

I'm late, aren't I?
I'm arriving late at night, aren't I? 

Note: Although it is technically "accepted" amongst English speakers,  strictly grammatically speaking, it should be  as follows:

I'm late, am I not?
I'm arriving late at night, am I not? 

Again, pretty much everyone in the United States will always use "aren't I" instead of "am I not", simply because that's the way they have always spoken. "Am I not" is considered by many, as an extremely formal way to address someone, rarely used in spoken English but only in written English, like in formal letters and such.

Negative statements with the verb "to be"

I'm not late, am I?
It isn't a beautiful day, is it?
Martha isn't angry, is she? 
You aren't really tired, are you? 
They aren't very nice people, are they? 
You aren't coming tomorrow, are you? 
Pedro isn't flying now, is he? 

Affirmative statements with the verb "to be" in simple past

It was a beautiful day, wasn't it?
Martha was angry, wasn't she? 
You were really tired, weren't you? 
You were studying at 6, weren't you? 
He was flying when I phoned, wasn't he? 

Affirmative statements with other common verbs

You went to Costa Rica in 1990, didn't you? 
Elena has traveled a lot, hasn't she? 
Ann will be here soon, won't she? 
Tom should pass his exam, shouldn't he?
You can play the violin, can't you?
He could find a job, couldn't he?

Imperative, suggestions and invitations

Let's go out for a walk, shall we? 
Let's study tomorrow morning, shall we?
Open the door, will you? 
Don't smoke in this room, will you?