Gavekortet ligger ved siden af fødselsdagskortet.

Because -et is the definite article for many neuter nouns in Danish.

• et gavekort = a gift card
• gavekortet = the gift card

And similarly:

• et fødselsdagskort = a birthday card
• fødselsdagskortet = the birthday card

So instead of putting a separate word like the in front, Danish often adds it to the end of the noun.

In Danish, the definite article is usually attached to the noun as a suffix.

So English:

• the gift card
• the birthday card

becomes Danish:

• gavekortet
• fødselsdagskortet

This is very normal in Danish. You usually learn nouns with their gender:

• en bil → bilen
• et hus → huset
• et kort → kortet

The sentence follows a very standard Danish word order:

Gavekortet + ligger + ved siden af fødselsdagskortet
subject + verb + location

So:

• Gavekortet = the subject
• ligger = the verb
• ved siden af fødselsdagskortet = a prepositional phrase telling you where it is

This is similar to simple English sentences like The book is on the table.

Danish often prefers a position verb where English might simply use is.

Here, ligger comes from ligge, which means to lie or to be lying/resting somewhere.

So Gavekortet ligger ved siden af fødselsdagskortet is more natural in Danish than using er.

This is a common pattern:

• Bogen ligger på bordet = The book is on the table
• Nøglerne ligger i tasken = The keys are in the bag

English often uses is/are, but Danish often uses verbs like:

• ligge = lie
• stå = stand
• sidde = sit

depending on how something is positioned.

Ligger is the present tense of ligge.

• at ligge = to lie / to be lying
• ligger = lies / is lying

So the sentence is in the present tense: The gift card is lying / is located next to the birthday card.

Ved siden af means next to or beside.

It is a fixed expression. Literally, it is something like by the side of, but you should learn it as a whole phrase meaning:

• next to
• beside

Examples:

• Stolen står ved siden af bordet = The chair is next to the table
• Hun sidder ved siden af mig = She is sitting next to me

Yes, that is the safest way to learn it.

Even though it is made up of several words, it functions as one expression meaning next to/beside.

So in this sentence:

• ved siden af fødselsdagskortet = next to the birthday card

It is better not to translate each word separately every time. Just recognize the whole chunk.

Because Danish, like English, often makes compound nouns, but Danish usually writes them as one word.

Here:

• fødselsdag = birthday
• kort = card
• fødselsdagskort = birthday card

Then the definite ending is added:

• fødselsdagskortet = the birthday card

The same thing happens in many Danish words. Compounds are extremely common, so getting used to long nouns is important.

You need to know the noun’s gender.

Danish common nouns usually have either:

• en-word (common gender)
• et-word (neuter)

If the noun is an et-word, the definite form often ends in -et:

• et kort → kortet
• et gavekort → gavekortet

If it is an en-word, the definite form often ends in -en:

• en bil → bilen
• en stol → stolen

So when you learn a noun, always learn it with en or et.

Yes, in this sentence the meaning is most naturally physical location: one card is placed next to the other.

The phrase ved siden af can sometimes appear in less literal contexts, but here, with two concrete objects, it clearly describes where the gift card is.

Yes, people would understand it, and it is not grammatically wrong. But ligger sounds more natural when talking about an object resting somewhere.

So:

• er ved siden af = understandable, more neutral
• ligger ved siden af = more idiomatic for an object like a card

Danish often sounds more natural when you choose the position verb that matches the object.

The indefinite forms are:

• et gavekort = a gift card
• et fødselsdagskort = a birthday card

The sentence uses the definite forms:

• gavekortet = the gift card
• fødselsdagskortet = the birthday card

So a very useful thing to practice is:

• et gavekort → gavekortet
• et fødselsdagskort → fødselsdagskortet