Læreren lægger en sort farveblyant på bordet ved siden af papiret.

In Danish, the definite article is often added to the end of the noun instead of being a separate word.

• lærer = teacher
• læreren = the teacher

This -en ending is the definite form for many common gender nouns.

So:

• en lærer = a teacher
• læreren = the teacher

This is one of the first big differences from English.

This is the difference between indefinite and definite nouns.

• en sort farveblyant = a black colored pencil
  This is indefinite: it is introducing the object as a pencil, not the pencil.

• bordet = the table
• papiret = the paper
  These are definite: a specific table and a specific paper are meant.

So the sentence mixes indefinite and definite nouns, just like English often does:

• The teacher puts a black colored pencil on the table beside the paper.

Because farveblyant is a common gender noun in Danish, and common gender nouns take en in the indefinite singular.

• en farveblyant = a colored pencil

Danish nouns have two grammatical genders:

• common gender → usually takes en
• neuter → takes et

In this sentence:

• farveblyant is common gender → en farveblyant
• bord is neuter → et bord
• papir is neuter → et papir

That is why their definite forms are:

• bordet = the table
• papiret = the paper

Sort is the adjective black.

Danish adjectives change form depending on the noun phrase. Here, sort is used with en ... farveblyant:

• en sort farveblyant = a black colored pencil

With this particular adjective, the singular indefinite form is sort.

Useful comparison:

• en sort blyant = a black pencil
• et sort bord = a black table
• sorte blyanter = black pencils
• den sorte blyant = the black pencil

So in this sentence, sort is the correct form.

It is a compound noun:

• farve = color
• blyant = pencil

So farveblyant literally means something like color pencil or colored pencil.

Danish uses compound nouns very often, much more freely than English. Instead of writing several separate words, Danish often joins them into one word.

Other examples of this pattern are common in Danish.

Lægger is the present tense of lægge, which often means to lay / put / place something down, usually in a lying or horizontal position.

• lægge = to lay, put, place
• lægger = lays / puts / places

In Danish, there can be a difference between:

• lægge = put something down so it lies
• sætte = set something somewhere, often more upright
• stille = place/set, often standing upright

A pencil on a table is naturally thought of as lying down, so lægger is very natural here.

Because it is in the present tense.

For many Danish verbs, the present tense is formed with -r or -er. Here:

• at lægge = to put / to lay
• lægger = puts / is putting

So:

• Læreren lægger ... = The teacher puts ...

Danish does not usually change the verb for different persons the way English does. The same present-tense form is used with different subjects:

• jeg lægger
• du lægger
• han/hun lægger
• vi lægger

Because this sentence is a normal main clause with the subject first. Danish often uses a word order that looks a lot like English in simple statements:

• Læreren = subject
• lægger = verb
• en sort farveblyant = object
• på bordet = prepositional phrase
• ved siden af papiret = another prepositional phrase

So the structure is:

Subject + Verb + Object + Place information

That gives:

Læreren lægger en sort farveblyant på bordet ved siden af papiret.

På usually means on.

So:

• på bordet = on the table

Breakdown:

• på = on
• bordet = the table

This tells you where the pencil is being placed.

Ved siden af is a fixed expression meaning beside, next to, or at the side of.

Breakdown:

• ved = by / at
• siden = the side
• af = of

Literally it is something like by the side of, which is close to English.

So:

• ved siden af papiret = beside the paper / next to the paper

You should learn ved siden af as a whole expression, not word by word only.

Because the phrase means beside the paper, not beside paper in a general sense.

• papir = paper
• papiret = the paper

So:

• ved siden af papiret = beside the paper

Danish often uses the definite form where English would also use the.

In normal understanding, it describes the location where the pencil is placed.

So the idea is:

• The teacher puts a black colored pencil on the table
• specifically, next to the paper

In other words, the pencil ends up on the table, and its position on the table is beside the paper.

Not in this exact phrase.

Danish usually puts definiteness directly on the noun:

• bordet = the table
• papiret = the paper
• læreren = the teacher

A separate word such as den or det is often used when there is an adjective before a definite noun:

• det sorte bord = the black table
• den sorte blyant = the black pencil

But when there is no adjective, Danish usually just uses the noun with the definite ending:

• bordet
• papiret
• læreren

A learner often notices that Danish spelling and pronunciation do not always match very clearly.

A rough guide:

• lægger sounds approximately like LEH-ger with a soft Danish g
• the æ is a front vowel somewhat like the vowel in English cat, but not exactly the same

You do not pronounce every letter as strongly as in English. Danish often weakens consonants in everyday speech.

If you are learning pronunciation, it is best to listen to native audio for:

• lærer
• læreren
• lægger

Those are common words, but their spoken forms can feel less transparent than their spelling suggests.

That is just a common structural difference between Danish and English.

In this sentence, Danish gives the main object first:

• en sort farveblyant

Then it adds location step by step:

• på bordet
• ved siden af papiret

This kind of build-up is very natural in Danish. English does the same quite often too:

• a black colored pencil
• on the table
• beside the paper

So although some details are different, the overall flow of information is actually quite familiar to an English speaker.