Learn Hardcore Polish: Wczoraj poszedłem z żoną do kina, a potem na spacer. - Yesterday I went to the cinema with my wife and then for a walk.

iść / pójść – to go (one specific movement, usually once, in one direction)
- past: szedłem / szłam (imperfective), poszedłem / poszłam (perfective)
chodzić – to go (habitually, repeatedly, or back-and-forth), past: chodziłem / chodziłam

In this sentence we talk about one completed event yesterday: you went (once) to the cinema.

poszedłem = I went (and this action is seen as a single, completed event)
szedłem would mean I was walking / I was going (emphasizing the process)
chodziłem do kina would mean I used to go to the cinema (habitually)

So poszedłem is chosen because it expresses a single, completed action in the past.

What does the ending -em in poszedłem tell me?

The ending -em in poszedłem shows:

Person: 1st person singular (I)
Gender: masculine (speaker is male)

The basic past tense pattern for iść / pójść is:

ja poszedłem – I went (male speaker)
ja poszłam – I went (female speaker)

So:

A man says: Wczoraj poszedłem…
A woman says: Wczoraj poszłam…

If I’m a woman, do I just change poszedłem to poszłam?

Yes.
Everything else in the sentence stays the same:

Male speaker:
Wczoraj poszedłem z żoną do kina, a potem na spacer.
Female speaker:
Wczoraj poszłam z żoną do kina, a potem na spacer.

Only the verb ending changes to reflect the gender of the speaker.

Why is there no ja (I) in the sentence?

In Polish, the subject pronoun (ja, ty, on, etc.) is often dropped, because the verb ending already shows who is doing the action.

Poszedłem already means I went (male).
Poszłam already means I went (female).

You can say Ja poszedłem…, but it is usually used only for emphasis or contrast, for example:

Ja poszedłem do kina, a on został w domu.
I went to the cinema, and he stayed at home.

Why is it z żoną and not z żona or z żonę?

The preposition z (with) usually takes the instrumental case in this meaning (with someone).

Nominative (dictionary form): żona (wife)
Instrumental singular: żoną

So:

z żoną = with (my/the) wife

z żona or z żonę are ungrammatical here because z + with someone requires the instrumental, which ends in -ą.

Can I say z moją żoną instead of z żoną?

Yes.

z żoną = with (my/the) wife (context usually makes it clear it’s your wife)
z moją żoną = with my wife (explicitly says my)

Here both are correct:

Wczoraj poszedłem z żoną do kina…
Wczoraj poszedłem z moją żoną do kina…

Notice that moją is also in the instrumental (feminine) to match żoną:

Nominative: moja żona
Instrumental: z moją żoną

Why is it do kina and not do kino or do kinie?

The preposition do (to, into) takes the genitive case.

Nominative: kino (cinema)
Genitive singular: kina

So:

do kina = to the cinema

do kino (nominative) and do kinie (locative) are wrong in this context, because do must be followed by genitive.

What’s the difference between do kina and w kinie?

do kina – to the cinema (movement towards the place)
w kinie – in/at the cinema (being inside the place)

Examples:

Wczoraj poszedłem do kina. – Yesterday I went to the cinema.
Wczoraj byłem w kinie. – Yesterday I was at the cinema.

Your sentence focuses on the action of going, so it uses do kina.

Why do we say na spacer and not do spaceru?

For many activities in Polish (walk, party, meeting, concert, etc.), the preposition na + accusative is used to mean to go for / to go to (an event/activity).

Nominative: spacer (a walk)
Accusative: spacer (same form here)

So:

na spacer = for a walk

do spaceru exists but is rare and means something else (more abstract, like for the purpose of a walk, in certain contexts). For to go for a walk, always say iść na spacer / pójść na spacer.

What’s the difference between i and a as conjunctions, and why is it a potem here?

Both i and a can be translated as and, but they are used a bit differently:

i – simple linking: and (often just adds another item or action)
a – often shows a contrast or a loose sequence; can be and, whereas, while in English, depending on context

In …do kina, a potem na spacer:

a links two parts that are in sequence (first cinema, then walk) and slightly separates them as two stages of the evening.
i potem would not be wrong, but a potem sounds more natural and common in narration.

So a potem is like saying and then / and afterwards with a small sense of next stage.

Can I change the word order, for example say Poszedłem wczoraj z żoną do kina?

Yes. Polish word order is relatively flexible, and many variants are possible, with only small differences in emphasis. For example:

Wczoraj poszedłem z żoną do kina, a potem na spacer.
Neutral, slight emphasis on yesterday.
Poszedłem wczoraj z żoną do kina, a potem na spacer.
Slightly more emphasis on I went, then adds yesterday.
Z żoną wczoraj poszedłem do kina, a potem na spacer.
Possible, with some emphasis on with my wife.

All of these are grammatically correct; the main information stays the same. The original version is the most neutral and natural-sounding.

How do I pronounce the special letters in wczoraj poszedłem z żoną?

Key points:

wczoraj
- wc = like vch together (short), close to v‑ch in sovch (but smoother)
- cz = like ch in church
- stress is on the first syllable: WCZO-raj
poszedłem
- sz = like sh in ship
- ę (in -łem) at the end: usually sounds close to -em, nasal is very light or disappears in fast speech: poszed-lem
żoną
- ż = like s in measure or zh
- ą at the end: nasal -on / -om sound; here close to żo-n or żo-m

Stress in Polish is almost always on the penultimate (second-to-last) syllable:

WCZO-raj
po-SZED-łem
ŻO-ną