So I have begun to start writing my own songs and I have a chord progression that would go nicely as a verse but I don't know what chords to go to for a chorus and when to bring the other chord progression back in. I hear my music teacher tell me that songs often change key halfway through but have no idea how to change key or to even tell what key I am in. I am confused and any help would be greatly appreciated.

I am going for a kind of rocky emo type of song (Don't know if there's such thing) so I don't know whether that would help dictate a change of key or not.
I would say like 30% of songs change key (just a guess)
Normally for a new section. Californication by RHCP changes from A minor (verse and chorus) to A major for the solo.
Also you could change from A Major to A minor or just borrow chords from A minor like G major

But why don't you just keep the chords the same for the chorus? Loads of songs do this.
Here's some ways you can do this.

- play the same chords highter up the neck maybe add some extensions
- simply change from a clean tone to a dirty one
- pick the chords
- change the strumming pattern
- have the drums open the hihat
- add a different vocal melody
- add a 2nd guitar playing a extra melody

You get the idea

Also it's common for the bridge to change key to add some tensions that want to resolve

For the last chorus try keeping the same chord progression but move it up a half tone, I think the hawaii five o theme does this
Most songs don't change keys. If you need a chorus, you can never go wrong with I-V-vi-IV or some derivative thereof or just use the same chord progression as the verse but change something else. There really is no right or wrong answer.

Finding the key is easy. You just have to find where the song resolves -- that is to say that it will gravitate towards a certain chord that sounds like it should be the end. If you play G-D-Em-C it sounds like a G chord should afterwards to resolve it.

There are many ways to change keys. You can change to an unrelated key if you like the contrast. Really all you are doing is changing the point of resolution to a different chord. A common technique is modulation -- playing the same chord progression but in a different key, usually a semitone or whole tone up. So if you play D-G-Bm-G, then you change to E-A-C#m-A. This can make the song sound more energetic. Usually in pop songs you modulate in the middle or towards the end and then stick with that key until the end. Examples would be songs like Love Story, Lookin Out My Back Door, One Tin Soldier, etc.
There's no such thing; there never was. Where I am going you cannot follow me now.
You don't need to change keys. It's not rare to have key changes in songs but it's not rare to just stay in one key all the time either. Actually, I would guess in modern pop it's more common to stay in one key all the time. There are even some songs that are based on just one chord progression that is used in all of the different sections.

Here are some examples of songs that use (mostly) the same progression all the time:

If songs have key changes in them, they usually happen when the section changes (for example the verse is in one key, the chorus is in another).

Pretty much all of the different sections in this song are in different keys. So when the section changes, there is also a modulation. But this frequent key changes are actually pretty rare in pop/rock music, unless we are talking about some more progressive stuff. Most of the time the key change happens in the beginning of the chorus or the bridge.

At one point it was common to have a key change before the last chorus, but this trick is not used that much any more. Most of the time it's a half or a whole step up and it's commonly used in "epic" songs like "Time to Say Goodbye". "Living on a Prayer" uses this trick a bit more "creatively" - the last chorus modulates one and a half step up (and there's also a cool 3/4 measure before the key change that makes it sound even more awesome ).

The most common key change in pop music is between parallel (for example C major and C minor) or relative keys (for example C major and A minor). Here is a recent thread about this: https://www.ultimate-guitar.com/forum/showthread.php?t=1717696

But if you don't know what key your song is in, I wouldn't really worry about key changes yet. You don't really even need to know about keys to write songs. Just come up with ideas that sound good after one another. The knowledge of keys doesn't necessarily make this any easier (though many times if you don't know what you are doing, it's usually best to try to come up with ideas in the same key because those will more likely work and sound less "forced" than changing the key). You still need to come up with ideas that sound close enough to work in the same song but different enough to not sound too repetitive. Of course the more you know about theory, the easier it is to understand what's happening in other songs. But yeah, if you want to write in a certain style, just listen to songs in that genre and figure out what's happening in them. Pay attention to the song structure and the transitions between the different sections if you are having trouble with coming up with another idea that would work in the same song.

If you want to know what key you are in, you just need to find the note/chord that sounds like home. That is called tonic and that is also your key. If the tonic chord is major, you are in a major key, and if it's minor, you are in a minor key. (You may want to look at the major/minor key thread that I mentioned earlier in this post.)
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