Jeg finder svømmebrillerne frem, før jeg går ned til vandet.

Here, finder svømmebrillerne frem means something like get the swimming goggles out or take the swimming goggles out so they are ready.

It is not just find in the sense of discovering where they are. The little word frem adds the idea of bringing something out or making it available.

So the nuance is:

• jeg finder svømmebrillerne = I find the swimming goggles
• jeg finder svømmebrillerne frem = I get the swimming goggles out / ready

Because this is a verb + particle combination, and in a main clause the particle often appears later in the sentence.

So you get:

• Jeg finder svømmebrillerne frem

But in an infinitive or other forms, you may see it more as a unit:

• at finde svømmebrillerne frem
• jeg har fundet svømmebrillerne frem

This is similar to English phrasal verbs such as take out or pick up, where the second part can move around.

Danish forms compound nouns very freely, much more than English does.

So:

• svømme = swim / swimming
• briller = glasses / goggles

Together they become:

• svømmebriller = swimming goggles

English writes swimming goggles as two words, but Danish normally writes this kind of compound as one word.

The ending -ne makes the noun definite plural, so svømmebrillerne means the swimming goggles.

Compare:

• en svømmebrille = a swimming goggle
• svømmebriller = swimming goggles
• svømmebrillerne = the swimming goggles

Danish usually adds definiteness directly to the noun instead of using a separate word like the.

Like English glasses or goggles, Danish often uses briller in the plural because it refers to something with two lenses.

So svømmebriller is the normal everyday word for swimming goggles.

A singular form, svømmebrille, does exist grammatically, but in normal use people usually talk about the pair in the plural.

Because før jeg går ned til vandet is a subordinate clause, and many Danish writers put a comma before a subordinate clause.

So the sentence is divided into:

• main clause: Jeg finder svømmebrillerne frem
• subordinate clause: før jeg går ned til vandet

A useful thing to know: in modern Danish, some people omit this comma, depending on the comma system they follow. So you may also see:

• Jeg finder svømmebrillerne frem før jeg går ned til vandet.

Both can occur.

Because før introduces a subordinate clause, and subordinate clauses do not use main-clause word order.

In a normal main clause, Danish is a verb-second language:

• Jeg går ned til vandet
• Nu går jeg ned til vandet

But after a subordinating word like før, the clause keeps normal subject + verb order:

• før jeg går ned til vandet

So før går jeg would sound wrong here.

Danish often uses the present tense for:

• habitual actions
• general routines
• near-future actions

So før jeg går ned til vandet can mean:

• before I go down to the water
• before I am going down to the water
• before I head down to the water

English does something similar in clauses with before, when, and after:

• Before I go down to the water

So this present tense is very natural here.

Ned means down, so går ned til vandet is literally go down to the water.

Sometimes this is truly physical, because the water is at a lower point. But Danish also often uses ned in a very natural, almost idiomatic way for movement toward places like:

• ned til stranden = down to the beach
• ned til havnen = down to the harbor
• ned til vandet = down to the water

So even if the geography is not dramatically lower, ned can still sound perfectly natural.

Because til means movement to a place, while i means being or going in something.

So:

• gå ned til vandet = go down to the water
• gå i vandet = go into the water

In your sentence, the speaker is only going to the water’s edge at that point, not necessarily entering the water yet.

Because each clause needs its own subject.

The sentence has two clauses:

• Jeg finder svømmebrillerne frem
• før jeg går ned til vandet

So Danish repeats jeg, just as English does:

• I get the swimming goggles out before I go down to the water

You cannot normally leave out the second jeg here.