Hun skjærer en sitron og legger den i vannet.

Hun is the subject form of she. It is used for the person doing the action.

• Hun skjærer ... = She cuts ...

Henne is the object form of her, and it would be used when something happens to her.

• Jeg ser henne. = I see her.

So in this sentence, she is the one performing the actions, so hun is correct.

They are both in the present tense.

• å skjære = to cut
• skjærer = cuts / is cutting
• å legge = to put / lay
• legger = puts / is putting

In Norwegian, the present tense is often made by adding -r to the infinitive stem:

• skjære → skjærer
• legge → legger

So the sentence has two present-tense actions joined by og:

• Hun skjærer en sitron og legger den i vannet.

That is like saying:

• She cuts a lemon and puts it in the water.

Because legger is a finite verb, not an infinitive.

Å is used with the infinitive form:

• å skjære
• å legge

But in the sentence, the verbs are conjugated to match the subject and tense:

• Hun skjærer ...
• ... og legger ...

English does the same:

• She cuts and puts ... not
• She cuts and to put ...

So after og, you just use another normal verb form if it shares the same subject.

Because sitron is a common-gender noun in Norwegian, so its indefinite article is en.

• en sitron = a lemon

Norwegian nouns have grammatical gender, and that affects the article:

• en for many masculine/feminine nouns in Bokmål common gender
• et for neuter nouns

So:

• en sitron
• but, for example, et eple

Because den refers back to en sitron, which is a common-gender noun.

In Norwegian, pronouns like it often match the grammatical gender of the noun:

• en sitron → den
• et eple → det

So:

• Hun skjærer en sitron og legger den i vannet. = She cuts a lemon and puts it in the water.

If the noun had been neuter, you would use det instead.

Vannet is the definite form: the water.

• vann = water
• vannet = the water

Norwegian often adds the definite article as an ending on the noun:

• en bil → bilen
• et hus → huset
• vann → vannet

Here, i vannet means in the water.

Because vann is a neuter noun, and the definite singular ending for many neuter nouns is -et.

So:

• et vann = a water / a lake in some contexts, but vann is also used as the general substance water
• vannet = the water

This is part of a common pattern:

• et eple → eplet
• et hus → huset
• vannet

So the ending shows definiteness.

In this sentence, it can naturally be understood as into the water because of the action legger.

Norwegian often uses i where English might choose either in or into, depending on context.

• legger den i vannet = puts it in/into the water

The motion is understood from the verb legger. English usually makes that distinction more explicitly, but Norwegian often does not need to.

Because this is a simple main clause with the normal Norwegian pattern:

Subject + verb + object

• Hun = subject
• skjærer = verb
• en sitron = object

Then another coordinated verb phrase:

• og legger den i vannet

So the overall structure is very close to English:

• She cuts a lemon and puts it in the water.

That said, Norwegian word order changes more noticeably when another element comes first. For example:

• I vannet legger hun den.

Then the verb still comes in the second position, which is a very important Norwegian rule.

Both can often mean to cut, but skjære is very common for slicing or cutting with a knife, especially with food.

• skjære en sitron = cut/slice a lemon

Kutte is also common and can mean cut, but it is often a bit broader and can sound more like cut off, cut up, or just general cutting depending on context.

For a lemon, skjære sounds very natural.

Legge is often used when placing something down, especially something that ends up lying somewhere.

• legge den i vannet = put it in the water

Related verbs:

• sette often suggests setting something upright or placing it in position
• putte often means put in a more general, informal sense, especially into something

So:

• Hun legger den i vannet is natural and standard.
• Hun putter den i vannet would also be possible, but it sounds a bit more like she puts it into the water in a general sense.
• sette would be less natural for a lemon slice.

This is a word many learners find tricky because of skj.

A rough guide:

• skj is pronounced like a soft sh sound in many dialects
• æ is like the vowel in bad for many English speakers, though not exactly the same
• rer at the end may sound lighter depending on dialect

A rough approximation might be:

• SHAIR-er

But this is only approximate. The main challenge is that skj, sj, and some kj sounds can be difficult for English speakers, and pronunciation varies a bit by dialect.

Yes. The Norwegian present tense can describe both:

• something happening right now
• something that happens regularly
• a general process or instruction-like action

So Hun skjærer en sitron og legger den i vannet could mean:

• She is cutting a lemon and putting it in the water
  or
• She cuts a lemon and puts it in the water

The exact meaning depends on context, just like in some English situations.