人很忙

I am busy.

I'm really busy.
I'm kind of busy.
She is sort of busy.
We will be unbelievably busy next week.
They were so busy yesterday.
Mark might be a little busy tomorrow.

I'm busy as a bee.

Since bees are always flying around here and there working, we often use this expression to show that we are busy.

I'm slammed.

I'm so busy (that) I can't even...

We can use this common sentence pattern to show how busy we are. The second part of this changes a lot. We can also make our own unique sentence.
I'm so busy that I can't even go to the bathroom.
I'm so busy that I can't even go to lunch.
I'm so busy that I can't even go home tonight.
I'm so busy that I can't even think.
We can make other similar sentences.
I am so busy that I don't even have time to eat.
She is so busy that she didn't have time to go to her mother's birthday party.

I'm buried in work.

I'm overwhelmed.

I'm up to my ears in (something).

I'm preoccupied at the moment.

I've got a lot on my plate.

My schedule is full.

I've got too much going on.

I've got a lot to do.

I'm tied up right now.

I'm swamped.

Quarterly tax time has got me swamped.
每季度一到交税 我就忙得不可开交。

I’m really swamped with work stuff.
我工作整天忙死了。

I'm knee-deep in (something).

物（城市）忙

It's crowded.

This is the basic way to say that a place is busy and that there are many people.

It's packed.

We use this expression when a place is very busy and very crowded. This can be used in a positive or negative way.
The store was packed. It was hard to move.
The club was packed. It was so much fun.

It's a madhouse.

In this expression, "mad" means "crazy". "Madhouse" is slang for a hospital where mentally ill patients are kept. To say that a place is "a madhouse", then we are saying it is crazy how busy the place is. We usually this expression in a negative way.
The store was a madhouse. It was terrible.

It's lively.

This expression shows that a place has a lot of people and has a lot of energy. We usually use this in a positive way. If a place is "lively" that is a good thing.

It's bustling.

This means that there are a lot of people and a lot of activity happening in a place.

一天忙

It is hectic.

We use this expression when we have many things and activities to do. "Hectic" means to be very busy and full of activity.
We also use the word "hectic" to talk about our day.
Yesterday was hectic.
Today is so hectic.

It is packed.

When used to talk about one's schedule, then this means that our schedule is full.

It is full.

This is another basic way to show that we have a busy schedule.