doing pretty good

[How's it going?] Doing pretty good.

We can give the answer 'doing pretty good' when we are asked how we are feeling.  Technically this is not grammatically correct, but it is very commonly used.  Notice the following:

1. She is doing pretty good at her new job.
   
2. I am actually doing pretty good now.
   

introduce yourself

Could you introduce yourself, please?

When we 'introduce ourselves' we say our name and maybe a little bit about ourselves, like where we are from or what hobbies we have.  Notice the following:

1. Please introduce yourself to the class.
   
2. I always hated introducing myself in school classes.
   

short time

I lived in Wyoming for a really short time.

A 'short time' is a small amount of time.  The actual amount of time changes depending on the situation. In the example, a short time is probably a few weeks or months, but if you wait a short time for a bus it is probably a few minutes.  Notice the following:

1. She was only here for a short time before she left again.
   
2. We lived in a hotel for a short time at first.
   

of those

Of those three states, which one is the best?

We use the phrase 'of those' to refer back to some different options that were stated already in the conversation.  We use this phrase so we don't have to repeat what has already been said.  Notice the following:

1. Of those restaurants, which is your favorite?
   
2. Of those countries, which was the most beautiful?
   

lots of nature

Oregon and Washington State have lots of nature.

'Nature' is natural aspects such as trees, lakes, rivers and animals.  There is 'lots of nature' in a natural place.  Notice the following:

1. There is lots of nature around the school.
   
2. Does your area have lots of nature?