Learn Hardcore Czech: Dnes půjdu do práce pěšky, protože autobus je plný lidí. - Today I will go to work on foot because the bus is full of people.

The verb jít is irregular in this way, just like jet → pojedu (to go by vehicle). For most other imperfective verbs you do use budu + infinitive (e.g. budu pracovat, budu číst, budu vařit).

Could I also say Dnes jdu do práce pěšky instead of Dnes půjdu do práce pěšky?

Yes, you can. Both are correct, but there is a nuance:

Dnes jdu do práce pěšky.
- Literally present tense, but very often used for a planned or arranged near‑future action (similar to English “I’m going to work on foot today.”).
- Feels a bit more like a fixed plan or something already decided and arranged.
Dnes půjdu do práce pěšky.
- Clear future tense, focusing on the decision about what will happen later today.
- Often sounds like a choice or resolution, sometimes even made just now: “You know what, today I’ll walk.”

Both sentences are natural; the difference is subtle and mostly about feel and context, not about correctness.

What is the difference between půjdu and pojedu?

These two verbs differ in the mode of transport:

půjdu – I will go on foot (walk)
pojedu – I will go by some vehicle (bus, car, train, etc.)

Examples:

Dnes půjdu do práce pěšky. – Today I will walk to work.
Dnes pojedu do práce autobusem. – Today I will go to work by bus.

So in your sentence, půjdu fits because the speaker explicitly says pěšky (“on foot”).

Why is it do práce and not na práci or k práci, and what case is práce here?

The key is the preposition do, which normally means “to / into” and takes the genitive case.

do + GEN: direction into or to a place
- do práce – to (my) workplace
- do školy – to school
- do města – to town

Práce is a feminine noun whose nominative singular and genitive singular look the same:

Nominative sg: práce (the work / job)
Genitive sg: práce (of work / to work, after do)

So in do práce, práce is genitive singular required by do.

Why not the others?

na práci – usually “for work” (for a task), not “to my workplace”:
- To je dobré na práci. – That’s good for work.
k práci – “towards work / to the work (as a task)”, very unusual for “to my job”.

For “to work” meaning “to my workplace”, do práce is the standard phrase.

What exactly does pěšky mean, and what kind of word is it?

Pěšky is an adverb and means “on foot”.

It doesn’t change for gender, number, or case.
It normally appears with verbs of movement like jít, chodit:
- Jdu do práce pěšky. – I’m going to work on foot.
- Často chodím do školy pěšky. – I often walk to school.

Don’t confuse it with pěší:

pěší is an adjective meaning “pedestrian”:
- pěší zóna – pedestrian zone
- pěší turista – a hiker (literally “pedestrian tourist”)

You say jdu pěšky, not jdu pěší.

Why is it autobus and not autobusem in protože autobus je plný lidí?

Here, autobus is the subject of the clause:

autobus je plný lidí = the bus is full of people

Subjects are in the nominative case in Czech, so we use autobus (nominative singular).

Autobusem is the instrumental form and is used mainly to express means of transport:

Jedu autobusem. – I go / I’m going by bus.
Do práce jezdím autobusem. – I commute to work by bus.

In your sentence we are describing the bus itself, not saying we travel by bus, so nominative autobus is required.

Why is it plný lidí and not plný lidi or plný lidmi?

The adjective plný (“full”) normally takes a genitive complement:

plný čeho? – full of what?

So we need the genitive plural of lidé / lidi (“people”), which is lidí:

plný lidí – full of people
plný vody – full of water
plný práce – full of work

About the different forms:

lidé – standard nominative plural (“people” as subject)
- Lidé jsou unavení. – People are tired.
lidi – colloquial nominative/accusative plural (“people”)
- Znám ti ty lidi. – I know those people. (colloquial)
lidí – genitive plural (“of people”) – this is what we need after plný
- plný lidí – full of people
lidmi – instrumental plural (“with / by people”)
- Obklopený lidmi. – Surrounded by people.

So plný lidí is the only correct option here.

How do I know that lidí is genitive plural, not something else?

Mainly from two things:

The adjective it follows:
plný almost always takes genitive:
- plný lidí, plný vody, plný problémů.
Patterns of the noun “lidé / lidi”:
For “people” we have:
- Nom. pl.: lidé (standard) / lidi (colloquial)
- Gen. pl.: lidí
- Dat. pl.: lidem
- Acc. pl.: lidi / lid (the latter is rare/archaic)
- Loc. pl.: lidech
- Instr. pl.: lidmi

The combination plný + lidí fits the genitive pattern “full of X” perfectly.

Why is there a comma before protože?

In Czech, when protože connects two clauses (main clause + reason clause), you normally must write a comma before it:

Dnes půjdu do práce pěšky, protože autobus je plný lidí.
Nešel jsem ven, protože pršelo.

Protože is a subordinating conjunction (“because”), and standard Czech punctuation puts a comma before such conjunctions (protože, že, když, aby, jestli…) when they introduce a dependent clause.

So the comma in your sentence is required by normal punctuation rules.

Can the word order change? For example, can I say Půjdu dnes do práce pěšky, protože je autobus plný lidí?

Yes. Czech word order is relatively flexible, so several variants are correct and natural, just with slightly different emphasis.

All of these are fine:

Dnes půjdu do práce pěšky, protože autobus je plný lidí.
– Neutral, focuses on today at the beginning.
Půjdu dnes do práce pěšky, protože autobus je plný lidí.
– Similar meaning; light emphasis on půjdu (“I will go”).
Dnes půjdu do práce pěšky, protože je autobus plný lidí.
– Also correct; by saying protože je autobus plný lidí, you slightly emphasize the state “is full” as the explanation.

Less natural/marked (but still grammatical in the right context):

Dnes půjdu do práce pěšky, protože plný lidí je autobus.
– Strongly emphasizes autobus as the item that is full of people.

What you can’t do is break up fixed expressions in a strange way or make the clause-internal order too chaotic. But in your examples, moving dnes, pěšky, or je autobus around is mostly about information focus, not correctness.

Why is there no word for “the” or “a” in autobus or práce?

Czech simply does not have articles (no equivalents of English a / an / the as separate words in normal standard usage).

So:

autobus can mean the bus, a bus, or buses in general, depending on context.
do práce can mean to work, to my job, etc., again depending on context.

Czech speakers rely on:

Context (what has already been mentioned)
Word order and stress
Optional demonstratives (ten, ta, to, tenhle…) when they really need to specify something like “this/that bus”.

In your sentence, a natural English translation would use articles:

Today I will go to work on foot, because the bus is full of people.

But in Czech, no extra words are added.

After protože, should it be autobus je plný lidí or je autobus plný lidí? Is one more correct?

Both protože autobus je plný lidí and protože je autobus plný lidí are grammatically correct. The difference is mainly in emphasis and rhythm, not correctness.

protože autobus je plný lidí
- Straight subject–verb–complement order.
- Slightly more neutral and common in everyday speech.
protože je autobus plný lidí
- Verb comes before the subject.
- This can sound a bit more emphatic or stylistic, and in some contexts it may highlight the state (“is full”) more than the noun autobus.

Only if you started the sentence with Je autobus plný lidí?, that would be a question. But with protože in front, it is clearly not a question, just a reason clause, and both orders are allowed.