How do we say “I don’t walk” or “the teacher doesn’t go to school” or “the cat doesn’t eat the food” or “this isn’t big”?

What you have to do in these sentences is negate the verb or adjective. You can do this in two different ways:

1. 안 + verb or adjective - 다 + 아요/어요/여요
안 means “not”
2. Verb or adjective - 다 + 지 않아요
않다 means “to not do.” Although it itself is a verb, it can also be used for both verbs and adjectives (can be used to say something doesn’t do or isn’t something)
1. Let’s look at the sentences above negated using the first method:

저는 안 걸어요 = I do not walk
선생님은 학교에 안 가요 = The teacher does not go to school
고양이는 음식을 안 먹어요 = The cat does not eat the food
이건 안 커요 = This is not big
*Notice how 안 goes right before the verb or adjective being negated. Essentially, just conjugate the verb or adjective the way you normally would and add 안 before it!

2. Let’s look at them using the second method:

저는 걷지 않아요 = I do not walk
선생님은 학교에 가지 않아요 = The teacher does not go to school
고양이는 음식을 먹지 않아요 = The cat does not eat the food
이건 크지 않아요 = This is not big
*Don’t worry about what -지 means. On its own, it has no meaning and is used only for grammatical purposes like this!

To my knowledge, there’s really no difference in nuance between these two methods. The meanings are the same! (Someone please correct me if I’m wrong!)

There are some verbs and adjectives that you do not need to use either of these methods on. For instance, let’s look at 있다 (to have / to be there). You can say this:

연필이 있어요 = I have a pencil / There is a pencil
But I’ve never heard anyone say this to mean “I don’t have a pencil / There is not a pencil”:

연필이 안 있어요 (this sentence might actually mean something completely different, so don’t say this to say you don’t have a pencil!)
연필이 있지 않아요
Rather, you should use the verb 없다 (to not have / to not be there) and say this:

연필이 없어요 = I don’t have a pencil/there is no pencil
In short, if a verb or adjective ends in 있다, used 없다 to make it negative. Let’s look at another example:

한식은 맛있어요 = Korean food is delicious
Here, the adjective is 맛있다, meaning “to be delicious.” 맛 means “taste” or “flavor,” so it could literally mean “to have taste”/”to be flavorful.”

Thus, if we wanted to say that Korean food tastes bad (or has no taste, even), simply switch out the 있다 for 없다:

한식은 맛없어요 = Korean food doesn’t taste good

*A little note on pronunciation! 맛없다 would be pronounced mat-eop-da (the ㅅ remains as a “t” sound rather than becoming an “s” sound), while 맛있다 is pronounced ma-sheet-da. For some reason, the ㅅ in 맛없다 doesn’t follow the usual rules!