Než půjdeme k řece, vezmu si ručník a láhev vody.

Here než means before.

So:

Než půjdeme k řece = Before we go to the river

A useful extra note: než can also mean than in comparisons, but that is not its role in this sentence.

That is a very common difference between Czech and English.

In Czech, after než referring to a future action, it is normal to use a future form:

Než půjdeme k řece = literally Before we will go to the river, but natural English is Before we go to the river.

So the Czech grammar is correct here, even though English uses a present form.

Because půjdeme is the future of jít.

• jdeme = we are going / we go
• půjdeme = we will go

Since the sentence talks about something that will happen later, půjdeme is the right choice.

Yes. The verb jít usually means to go on foot or simply to go in a general movement sense.

So půjdeme k řece naturally suggests we’ll walk/go to the river.

If the idea were specifically go by vehicle, Czech would normally use jet instead.

Because k and do mean different kinds of movement.

• k řece = to/toward the river, usually meaning the riverbank area
• do řeky = into the river

So in this sentence, k řece means going to the river as a destination, not going into the water.

Because the preposition k requires the dative case.

The noun changes like this:

• řeka = nominative singular
• řece = dative singular

So:

k řece = to the river

You may also notice the stem change k → c, which is a normal sound change in Czech declension.

Vzít si is a very common Czech expression meaning to take, often with the sense of take for oneself / take along / pick up for one’s own use.

So:

• vezmu = I will take
• vezmu si = I will take for myself / I’ll take

In a sentence like this, vezmu si ručník sounds very natural, because the speaker is taking the towel for their own use.

Formally, it is a present-tense form of a perfective verb, but in meaning it refers to the future.

The verb is vzít, which is perfective. In Czech, perfective verbs do not normally have a true present meaning. Their present forms usually express a completed action in the future.

So:

• vezmu = I will take
• not I am taking

This is an important Czech pattern.

They are the direct objects of vezmu si, so they are in the accusative case.

In this sentence:

• ručník is accusative singular
• láhev is accusative singular

But both happen to look the same as the dictionary form here:

• masculine inanimate ručník often has accusative = nominative
• feminine láhev also has accusative singular identical in form here

So even though they are in the accusative, they do not visibly change.

Because Czech uses the genitive after container words like bottle, glass, cup, etc.

So:

• láhev vody = a bottle of water
• literally bottle of water

Here:

• láhev is the main noun
• vody is genitive singular of voda

If you were taking just water directly, without bottle, then you would use the accusative:

Vezmu si vodu. = I’ll take water.

Yes, absolutely.

s sebou means with me / along. So:

Vezmu si s sebou ručník a láhev vody. = I’ll take a towel and a bottle of water with me.

In your original sentence, s sebou is omitted because the idea is already clear from context. Adding it gives a little extra emphasis to the idea of taking the items along.

Yes. Czech word order is fairly flexible.

The original sentence is a very natural neutral version:

Než půjdeme k řece, vezmu si ručník a láhev vody.

You could also say:

Vezmu si ručník a láhev vody, než půjdeme k řece.

But starting with the než clause is very natural because it sets the time frame first.

Also note that si is a clitic, so it usually stays near the beginning of its clause:

• vezmu si
• not usually something much more separated

Because Než půjdeme k řece is a subordinate clause, and Czech normally separates it from the main clause with a comma.

So the structure is:

• subordinate clause: Než půjdeme k řece
• main clause: vezmu si ručník a láhev vody

That is why the comma is there.

Because Czech has no articles.

So nouns like ručník and láhev can mean:

• a towel / the towel
• a bottle / the bottle

The exact meaning depends on context.

That is normal in Czech, and learners have to get used to understanding definiteness from the situation rather than from separate words like a or the.