Půjdu zpátky do práce.

Půjdu means I will go.

It comes from the verb jít = to go (usually in the sense of one specific trip, on foot, in one direction).

This form is 1st person singular future:

• půjdu = I will go
• půjdeš = you will go
• půjde = he/she/it will go

So in this sentence, půjdu is the main verb and already tells you:

• the subject: I
• the tense: future

That is a very common question.

Many Czech verbs make the future with budu + infinitive, for example:

• budu pracovat = I will work

But jít is irregular. Its future is not normally made with budu jít. Instead, Czech uses special future forms:

• půjdu = I will go
• půjdeš = you will go
• půjde = he/she will go

So budu jít would sound unnatural in normal Czech.

Because Czech usually drops the subject pronoun when it is clear from the verb ending.

Here, půjdu already means I will go, so já is not necessary.

You could say:

• Já půjdu zpátky do práce.

But that would usually add emphasis, something like:

• I’ll go back to work.
• As for me, I’ll go back to work.

The neutral sentence is simply:

• Půjdu zpátky do práce.

Zpátky means back.

So it adds the idea of returning:

• Půjdu do práce = I will go to work
• Půjdu zpátky do práce = I will go back to work

It suggests that the speaker was away from work and is now returning.

A near synonym is zpět, which also means back, but zpátky is often a bit more conversational and common in everyday speech.

It is do práce because the preposition do takes the genitive case.

So:

• do
  • genitive = into / to

In Czech, going to work is expressed idiomatically as:

• jít do práce

The noun práce here is in the genitive singular.

A detail that can confuse learners:
the nominative singular and genitive singular of práce look the same:

• nominative: práce
• genitive: práce

So the case changes, but the form does not visibly change in spelling here.

Yes, literally do often means something like into, but Czech uses certain prepositions idiomatically with destinations.

With work, the normal expression is:

• jít do práce = to go to work

This is just the standard Czech pattern, much like:

• jít do školy = to go to school
• jít do kanceláře = to go to the office

So even though it may feel more literal as into work, the real idiomatic meaning is simply to work.

Here, práce most naturally means work in the sense of going to your job / place of work.

So do práce is best understood as:

• to work
• to my workplace
• back to my job

Czech often uses práce in this broad, practical way, just as English does in go to work.

This is an important distinction.

• jít = to go, in one specific instance, one direction
• chodit = to go regularly, repeatedly, habitually; also to walk around / to attend / to go somewhere as a routine

So:

• Půjdu zpátky do práce. = I will go back to work.
  One specific future return.

Compare:

• Chodím do práce. = I go to work / I commute to work.
  A habitual action.
• Budu chodit do práce. = I will be going to work / I will go to work regularly.
  A repeated future situation.

In your sentence, jít is used because it refers to one return trip.

Yes, Czech word order is fairly flexible, but different orders change the focus or emphasis.

The most neutral version is:

• Půjdu zpátky do práce.

You may also hear:

• Zpátky půjdu do práce.
  This emphasizes back.
• Do práce půjdu zpátky.
  Possible in context, but less neutral and more marked.

For a learner, the safest and most natural choice is:

• Půjdu zpátky do práce.

A rough pronunciation guide:

• Půjdu ≈ POOY-doo
• zpátky ≈ SPAAT-kee
• do ≈ doh
• práce ≈ PRAA-tseh

A few helpful notes:

• Czech stress is usually on the first syllable of each word.
• ů sounds like a long oo.
• j sounds like English y in yes.
• á is a long vowel.
• c in Czech is pronounced ts.

So the whole sentence is roughly:

• POOY-doo SPAAT-kee doh PRAA-tseh

That is only an approximation, but it is a useful start.

Yes. A very common alternative is:

• Vrátím se do práce.

This also means I’ll return to work.

The difference is mainly in nuance:

• Půjdu zpátky do práce = I’ll go back to work
  Focuses on the movement: going back
• Vrátím se do práce = I’ll return to work
  Focuses more directly on the idea of returning

Both are natural.
Your original sentence is perfectly normal and everyday Czech.

Yes, depending on context, the most natural English translation might sometimes be I’m going back to work.

Grammatically, půjdu is a future form, so its basic meaning is I will go back to work. But English often uses the present continuous for planned future actions, while Czech still uses the future form.

So in real translation, either of these may fit:

• I will go back to work
• I’m going back to work

The exact choice depends on the situation and tone.