that

Use "that" to refer to something that a person just said:

A: I'm going to try to start a career as an actor.

B: So does that mean you're moving to L.A.?

Or you can talk about something that you heard on T.V. or radio using "that".

I was just about to (do something).

Use this expression to talk about something that you were planning to do next. For example, at work:

A: Hey, are you busy?

B: Actually, I was just about to leave. What do you need?

This expression is useful in situations where you're a little bit late doing something:

A: Hey, can you send me those sales projections?

B: Yes, sorry. I was just about to do that.

This makes it seem like you were already planning to send them soon, even if this person didn't remind you.

go into (a topic)

"Going into" a topic means to speak about it.

You can use this phrasal verb to talk about what someone said:

Did she go into any details about our new health benefits?

You can use this phrase to talk about what you're saying as it's happening:

Do you want me to go into a few more details?

There's another phrase which is similar:

I don't want to get into it.

"Getting into" a topic means talking about something that's complicated or annoying to explain.