Kiedy uczę się nowego wyrażenia, zapisuję jego znaczenie i przykład w zeszycie.

Because the verb here is uczyć się, which means to learn.

In Polish, uczyć by itself usually means to teach someone, while uczyć się means to learn / study.

• uczę = I teach
• uczę się = I learn / I am learning

So:

• Kiedy uczę się nowego wyrażenia... = When I learn/am learning a new expression...

The word się is a very common part of many Polish verbs, and you often just have to learn the full verb together with it.

Because uczyć się usually takes the genitive case.

The dictionary form is:

• nowe wyrażenie = a new expression

But after uczyć się, it changes to genitive:

• uczyć się czego? = to learn what?
• nowego wyrażenia = of a new expression

So:

• uczę się nowego wyrażenia

This is one of those patterns that learners need to memorize:

• uczyć się + genitive

Here it can be understood as when or whenever, but in natural English this sentence often has a habitual meaning, so whenever is often the best interpretation.

Because the whole sentence describes a repeated habit:

• Kiedy uczę się nowego wyrażenia, zapisuję...
• Whenever I learn a new expression, I write down...

If this were about one specific occasion, context would make that clear. On its own, this sentence sounds like a general routine.

Because Polish often uses the present tense to describe a regular habit, just like English does.

Here the speaker is talking about something they generally do:

• uczę się = I learn / I am learning
• zapisuję = I write down / I am writing down

So the sentence means something like:

• Whenever I learn a new expression, I write down its meaning and an example in my notebook.

Also, both verbs are imperfective, which fits a repeated, ongoing habit very well.

Because Kiedy uczę się nowego wyrażenia is a subordinate clause, and in Polish subordinate clauses are normally separated by a comma.

So the structure is:

• Kiedy uczę się nowego wyrażenia, = When/Whenever I learn a new expression,
• zapisuję jego znaczenie i przykład w zeszycie. = I write down its meaning and an example in a notebook.

Polish uses commas more regularly than English in sentences like this, so this comma is required.

Jego here means its.

It refers back to wyrażenie (expression):

• wyrażenie = expression
• jego znaczenie = its meaning

Even though jego can also mean his, the context makes it clear that here it means its, because it refers to wyrażenie, which is a thing, not a person.

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

You are writing down:

• co? = what?
• znaczenie i przykład

However, the forms look the same as the dictionary forms here:

• znaczenie stays znaczenie
• przykład stays przykład

That is because for these nouns, the accusative singular is the same in form as the nominative singular.

So even though the case has changed grammatically, the visible form has not.

Because the preposition w meaning in requires the locative case when it refers to location.

The dictionary form is:

• zeszyt = notebook / exercise book

After w, it becomes:

• w zeszycie = in the notebook / in a notebook

So this is another useful pattern to learn:

• w + locative for location

Examples:

• w domu = in the house / at home
• w szkole = at school
• w zeszycie = in the notebook

Yes. Polish word order is more flexible than English word order.

The original sentence is natural and neutral:

• Kiedy uczę się nowego wyrażenia, zapisuję jego znaczenie i przykład w zeszycie.

But you could also move things around for emphasis, for example:

• Kiedy uczę się nowego wyrażenia, w zeszycie zapisuję jego znaczenie i przykład.
• Jego znaczenie i przykład zapisuję w zeszycie, kiedy uczę się nowego wyrażenia.

These versions are still understandable, but the original sounds the most straightforward and natural for a neutral statement.

So yes, word order can change, but it often changes emphasis rather than basic meaning.

Polish has no articles, so there is no direct equivalent of English a/an and the in most sentences.

That means:

• nowego wyrażenia can mean a new expression or sometimes the new expression, depending on context
• przykład can mean an example or the example
• w zeszycie can mean in a notebook or in the notebook

English has to choose between a and the, but Polish usually leaves that to context.

Zapisuję is the 1st person singular present form of zapisywać, which means to write down, to note down, or to record in writing.

So:

• zapisywać = to write down
• zapisuję = I write down / I am writing down

This verb is a very natural choice here because the speaker is noting something in a notebook.

It is also imperfective, which fits a repeated habit:

• Whenever I learn..., I write down...

A perfective form such as zapiszę would usually point more toward a single completed act in the future, not a general routine.

A rough English-friendly guide:

• Kiedy ≈ KYEN-dy
• uczę się ≈ OO-cheng shenh
  
  • the final vowel in uczę is nasal, so it is not exactly like English
• nowego ≈ no-VE-go
• wyrażenia ≈ vy-ra-ZHE-nya
• zapisuję ≈ za-pee-SOO-yeh
• znaczenie ≈ zna-CHEN-yeh
• przykład ≈ PSHI-kwat
• w zeszycie ≈ v zhe-SHYE-cheh

A few useful sound notes:

• wy often sounds roughly like vɨ; English has no exact equivalent
• rz here sounds like zh in measure
• cz sounds like ch, but harder and more retroflex
• sz sounds like sh
• w in Polish sounds like English v

Also, Polish stress is usually on the second-to-last syllable:

• wy-ra-ŻE-nia
• za-pi-SU-ję
• ze-SZY-cie