Jag lägger pepparn i soppan.

Lägger is the present tense form of the verb lägga.

• lägga = to put / to lay
• jag lägger = I put / I am putting

So in a normal statement with jag, you need the finite verb lägger:

• Jag lägger pepparn i soppan. = I put the pepper in the soup.

The infinitive lägga is what you would use after another verb, for example:

• Jag vill lägga pepparn i soppan. = I want to put the pepper in the soup.

The dictionary form is lägga.

A few useful forms are:

• infinitive: lägga
• present: lägger
• past: lade or la
• supine: lagt

Examples:

• Jag lägger pepparn i soppan. = I put/am putting the pepper in the soup.
• Jag lade pepparn i soppan. = I put the pepper in the soup.
• Jag har lagt pepparn i soppan. = I have put the pepper in the soup.

Because pepparn is the definite singular form: the pepper.

In Swedish, the definite article is usually attached to the end of the noun.

• peppar = pepper
• pepparn = the pepper

So:

• Jag lägger peppar i soppan. = I put pepper in the soup.
  This sounds more like pepper in general, as a substance.
• Jag lägger pepparn i soppan. = I put the pepper in the soup.
  This refers to a specific pepper, or the pepper already being talked about.

Soppan is the normal Swedish way to say the soup.

• soppa = a soup / soup
• soppan = the soup

Swedish usually makes nouns definite by adding an ending:

• en bok = a book
• boken = the book

So here:

• i soppan = in the soup

You would not normally say den soppa by itself.
Den is used with an adjective:

• den varma soppan = the hot soup

Because Swedish usually puts the at the end of the noun instead of using a separate article.

In this sentence:

• pepparn = the pepper
• soppan = the soup

This is one of the biggest differences from English.
Compare:

• English: the pepper

• Swedish: pepparn

• English: the soup
• Swedish: soppan

If there is an adjective, Swedish often uses both a separate word and the ending:

• den heta soppan = the hot soup

Yes. i usually means in.

So:

• i soppan = in the soup

That makes sense here because the pepper is being put into the soup.

Compare:

• på bordet = on the table
• i skålen = in the bowl
• i soppan = in the soup

English sometimes says put pepper in the soup, and Swedish works very similarly here.

In this sentence, peppar is most naturally understood as pepper the spice/seasoning.

That is because it goes naturally with soup:

• Jag lägger pepparn i soppan.

If you wanted to talk about a bell pepper / chili pepper, Swedish often uses more specific words, for example:

• paprika = bell pepper / paprika
• chili = chili pepper

So in this sentence, a learner should normally read pepparn as the pepper seasoning.

This is the normal word order for a basic Swedish main clause:

subject + verb + object + place/prepositional phrase

So here:

• Jag = subject
• lägger = verb
• pepparn = object
• i soppan = prepositional phrase

This is very similar to English:

• I put the pepper in the soup.

Swedish main clauses also follow the V2 rule, which means the finite verb usually comes in the second position. In this simple sentence, that gives:

• Jag lägger ...

Yes, Swedish can move parts of the sentence to the front for emphasis or style, but then the verb still has to stay in second position.

So you can say:

• I soppan lägger jag pepparn.

This puts extra focus on i soppan.

Notice what happens:

• normal order: Jag lägger pepparn i soppan.
• fronted phrase: I soppan lägger jag pepparn.

The verb lägger still comes second. That is the V2 rule in action.

It can cover all of those, depending on context.

Swedish present tense often matches both English simple present and present progressive:

• Jag lägger pepparn i soppan.
  • I put the pepper in the soup.
  • I am putting the pepper in the soup.

Which one sounds best in English depends on the situation.

Also, lägga often overlaps with English put and lay. In everyday translation, put is usually the most natural choice here.

No, Swedish normally does not drop the subject pronoun in ordinary sentences.

So you say:

• Jag lägger pepparn i soppan.

Not just:

• Lägger pepparn i soppan
  unless the subject is understood in a special context, such as informal notes, instructions, or spoken fragments.

In normal grammar, Swedish wants the subject to be stated.

A rough guide is:

• Jag ≈ yahg or sometimes almost ya
• lägger ≈ LEG-er with a short e
• pepparn ≈ PEP-parn
• i ≈ ee
• soppan ≈ SOP-pan

A few useful notes:

• ä sounds somewhat like the e in bed
• j in Swedish is usually like English y
• the -rn in pepparn may sound slightly merged in natural speech
• the stress is usually on the first syllable of lägger, pepparn, and soppan

Sometimes, but it is not the same in tone.

• lägga = put, lay
• tillsätta = add

So:

• Jag lägger pepparn i soppan. = I put the pepper in the soup.
• Jag tillsätter peppar i soppan. = I add pepper to the soup.

Tillsätta sounds a bit more formal or deliberate, while lägga is a very everyday verb. In ordinary conversation, lägger is completely natural.