“Amy and I were sitting there talking and this guy I know walked by.”

Something interesting happened to you yesterday while you were having lunch with your friend Amy. Now you are going to tell the story to another friend who wasn't there. You start the story by explaining the situation and what happened:

Amy and I were sitting there talking and this guy I know walked by.

(someone) and I

When you talk about yourself and another person, there are certain rules in English for which comes first - you or the other person:

• In casual conversation, many people say "Me and ___ (did something)." But some other people would never say this and would think it sounds uneducated. ("Me and Amy were sitting there...")
• In polite speech and in writing, it's considered correct to say "___ and I (did something)." ("Amy and I were sitting there...")
• Things get confusing when you put this at the end of a sentence. A lot of people still say "(do something) to ___ and I." But some people think this is incorrect and you should say "(do something) to ___ and me." Since everyone disagrees, you can probably just pick which one you like! "He said something to Amy and I / Amy and me.")

sitting (somewhere) (doing something)

You can combine "sitting" or "standing" with another action in this way. A few more examples:

I was sitting on the couch doing my homework.

They're still standing outside the train station waiting for someone.

Describing an action in this way with "sitting" or "standing" makes it sound like the action wasn't very important or interesting. This kind of phrase is often used to set up a story, like in the example above.

this (person/thing)

In the example above, the speaker says "this guy I know" instead of "a guy I know". There's a small difference between the two. When you say "this guy" it sounds like you're talking about a specific guy. "A guy" is more general. The identity of the person isn't important. Here's another example:

I saw this movie the other day.

When you say this, it sounds like you're going to explain something about the movie.

I saw a movie the other day.

This sounds like you're not interested in talking about the movie, but maybe just saying this as background for talking about something else.

a guy

"A guy" is a casual way of referring to a man. You use this word instead of "man" when you're talking to your friends or people you know well. The person you're talking about can either be someone that you know, or someone that you don't know but don't have high respect for. For a stranger who seems older and more respectable, you should use "man" or even "gentleman" for someone you really think highly of.

a (person) (someone) knows

"An acquaintance" is a person you know who's not close enough to be called a "friend". But the word "acquaintance" is pretty formal. When you're telling a story or talking to a friend, it's more natural to say "a person I know", "a woman he knows", "this guy she knew", etc.