Learn Hardcore German: Nächsten Sommer feiern wir eine kleine Hochzeit im Garten meiner Eltern. - Next summer we are celebrating a small wedding in my parents’ garden.

Sommer is masculine.
There is no article (der / ein) in front of it.
For a masculine noun in the accusative with no article, the adjective takes the ending -en → nächsten Sommer.

German often uses the accusative for time expressions (sometimes called the “accusative of time”):

Nächsten Sommer feiern wir … – We’ll celebrate next summer…
Jeden Tag lerne ich Deutsch. – I study German every day.

If Sommer were the subject, it would be nominative, and then you’d say:

Nächster Sommer wird schön. – Next summer will be nice.

So:

As a time expression → (den) nächsten Sommer
As a subject → nächster Sommer

Why is nächsten written with a capital N at the beginning of the sentence?

At the start of a sentence, every first word is capitalized in German, no matter what it is.

Inside a sentence, it would be:

Wir feiern nächsten Sommer eine kleine Hochzeit.

Only nouns (like Sommer, Hochzeit, Garten, Eltern) are normally capitalized in the middle of a sentence. Adjectives like nächsten, kleine are normally lower-case unless they are the first word of the sentence or used as a nominalized noun (e.g. im Allgemeinen).

Why does the verb come second: Nächsten Sommer feiern wir … and not directly after the subject?

In a main clause, German word order follows the rule “the conjugated verb is always in second position”.

The first position can be:

the subject: Wir feiern nächsten Sommer …
a time phrase: Nächsten Sommer feiern wir …
some other element you want to emphasize.

So both are correct:

Wir feiern nächsten Sommer eine kleine Hochzeit.
Nächsten Sommer feiern wir eine kleine Hochzeit.

When you move nächsten Sommer to the front, the verb (feiern) must still stay in second position, so the subject (wir) moves after the verb.

Is feiern here present tense or future? How can it talk about the future without werden?

Grammatically, feiern is in the present tense (Präsens).

However, German very often uses the present tense with a future time expression to talk about the future:

Nächsten Sommer feiern wir … – We’re celebrating / We’ll celebrate next summer …
Morgen fahre ich nach Berlin. – I’m going / I’ll go to Berlin tomorrow.

You can also use Futur I with werden:

Nächsten Sommer werden wir eine kleine Hochzeit feiern.

Both are correct, but the simple present + time expression is more common and more natural in everyday speech.

Why is it eine kleine Hochzeit and not something like ein kleines Hochzeit?

Because Hochzeit is a feminine noun in German: die Hochzeit.

For a feminine accusative singular noun with the indefinite article, you get:

Article: eine
Adjective ending: -e
Noun: Hochzeit

So: eine kleine Hochzeit

Compare:

Ich kaufe einen kleinen Tisch. – masc. acc. sg.
Ich kaufe eine kleine Tasche. – fem. acc. sg.
Ich kaufe ein kleines Auto. – neut. acc. sg.

Here, eine kleine Hochzeit is the direct object of feiern, so it’s in the accusative case.

Why do you use feiern with Hochzeit? Could you just say Wir heiraten?

You can say both, but they focus on slightly different things:

Wir heiraten nächsten Sommer.
- Focus: the act of getting married.
- Literally: We’re getting married next summer.
Nächsten Sommer feiern wir eine kleine Hochzeit.
- Focus: the celebration / event (the wedding party/ceremony).
- Literally: Next summer we are celebrating a small wedding.

So:

heiraten = to get married.
eine Hochzeit feiern = to celebrate the wedding (the event).

In many contexts, especially about the event in the garden, Hochzeit feiern sounds very natural.

What exactly is happening grammatically in im Garten meiner Eltern?

This phrase combines two things: a preposition + dative and a genitive.

im Garten
- in
  - dem (dative) → im
- Garten is masculine, dative singular: dem Garten → im Garten.
The preposition in takes dative when it expresses a location (where?):
- im Garten – in the garden (location)
- in den Garten – into the garden (movement, accusative)
meiner Eltern
- This is a genitive plural phrase meaning “of my parents”.
- Possessor: meine Eltern (plural).
- Genitive plural of meine Eltern is meiner Eltern (no -s on Eltern).

So structurally:

im Garten (dative: where?)
meiner Eltern (genitive: whose garden?)

Full breakdown:

im = in dem (prep. + dative)
Garten = masculine, dative singular
meiner Eltern = genitive plural of meine Eltern

Why is it meiner Eltern and not meinen Eltern?

Because meiner Eltern is genitive plural, not dative plural.

meinen Eltern would be dative plural: to my parents / for my parents.
meiner Eltern is genitive plural: of my parents.

In im Garten meiner Eltern:

Garten is the main noun.
meiner Eltern shows who owns the garden (the possessor).

This is the standard pattern for possession with a noun:

der Garten meiner Eltern – the garden of my parents
das Auto meines Bruders – my brother’s car
die Wohnung meiner Schwester – my sister’s flat

Can I also say im Garten von meinen Eltern instead of im Garten meiner Eltern?

Yes, im Garten von meinen Eltern is grammatically fine and very common in spoken German.

However, there is a nuance of style:

im Garten meiner Eltern
- Uses the genitive.
- Sounds a bit more formal / standard / written.
im Garten von meinen Eltern
- Uses von
  - dative instead of genitive.
- Very common in spoken, everyday German, slightly more colloquial.

So both are correct. For writing (especially more formal texts), im Garten meiner Eltern is usually preferred. In relaxed conversation, im Garten von meinen Eltern is very natural.

Could I change the word order at the end, e.g. Nächsten Sommer feiern wir im Garten meiner Eltern eine kleine Hochzeit?

Yes, that word order is also correct.

Two natural variants are:

Nächsten Sommer feiern wir eine kleine Hochzeit im Garten meiner Eltern.
Nächsten Sommer feiern wir im Garten meiner Eltern eine kleine Hochzeit.

German word order is fairly flexible. Some general tendencies:

Time information often comes early (as in this sentence).
The direct object (here: eine kleine Hochzeit) can come either before or after the place phrase (im Garten meiner Eltern).
The choice often depends on emphasis and what is already known in the conversation.

Both orders sound natural; version (1) feels slightly more neutral, because feiern eine kleine Hochzeit hangs together nicely as a unit, and the place comes after it.

Why is Sommer capitalized, but nächsten and kleine are not?

Because in German:

All nouns are capitalized: Sommer, Hochzeit, Garten, Eltern.
Adjectives like nächsten and kleine are normally lower-case.

So you write:

nächsten Sommer
eine kleine Hochzeit
im schönen Garten
meine lieben Eltern

The only reasons an adjective would be capitalized are:

It’s the first word of a sentence (e.g. Nächsten Sommer …).
It’s used as a noun (nominalized), e.g. im Allgemeinen, der/die Kleine.