Learn Hardcore Polish: Idź prosto do skrzyżowania i skręć w lewo przy banku. - Go straight to the intersection and turn left at the bank.

Idź is the 2nd‑person singular imperative of iść (to go on foot). Use Jedź (from jechać) when the person is going by vehicle: Jedź prosto do skrzyżowania i skręć w lewo przy banku. The verb skręć (turn) works for both walking and driving.

How do I say this politely/formally to a stranger?

Polish avoids the bare imperative with strangers. Two natural options:

Proszę iść prosto do skrzyżowania i skręcić w lewo przy banku.
Niech pan/pani idzie prosto do skrzyżowania i niech pan/pani skręci w lewo przy banku. Use pan to a man, pani to a woman. For a group: Niech państwo idą…/skręcą… or simply Proszę iść/skręcić….

How do I say it to more than one person?

Use plural imperatives: Idźcie prosto do skrzyżowania i skręćcie w lewo przy banku. For a formal group: Niech państwo idą… i skręcą…, or the polite Proszę iść/skręcić….

Why is it do skrzyżowania and not na skrzyżowanie?

Do means to, up to and takes the genitive case, so you use skrzyżowania. It tells you to go as far as the intersection. Na skrzyżowanie would literally be onto the intersection, which is not idiomatic here. If you want at the intersection, use na skrzyżowaniu (locative): Skręć w lewo na skrzyżowaniu.

What case is skrzyżowania, and why does it end in -a?

It’s genitive singular. The preposition do always takes genitive. The noun skrzyżowanie (neuter) has genitive singular skrzyżowania. The -a ending is standard for many neuter nouns in the genitive singular.

Why skręć and not skręcaj?

Polish uses perfective verbs for single, completed actions in instructions. Skręć (perfective, from skręcić) = make one turn. Skręcaj (imperfective) suggests repeated or ongoing turning (keep turning), so it sounds odd here.

Why w lewo instead of na lewo, and can I say just lewo?

In commands, the set phrase is skręć w lewo/w prawo.
Skręć na lewo is heard and understood, but w lewo is the safest, most standard choice for turning.
You cannot drop the preposition: Skręć lewo is ungrammatical in standard Polish.

What exactly does przy banku mean, and what case is banku?

Przy means by/at/near and takes the locative case, so bank becomes banku.

przy banku = at/by the bank (as a landmark)
w banku = inside the bank
obok/koło banku = next to the bank
przed bankiem = in front of the bank; za bankiem = behind the bank

How would I say Turn left at the first intersection?

Skręć w lewo na pierwszym skrzyżowaniu. You can also front it: Na pierwszym skrzyżowaniu skręć w lewo. Here na … skrzyżowaniu is locative (at the intersection).

Is the word order fixed? Could I say Prosto idź do skrzyżowania?

The neutral order is Idź prosto do skrzyżowania. Putting prosto first (Prosto idź…) sounds marked or odd in everyday speech. Adverbs like prosto normally follow the verb.

How can I say Go straight all the way to the intersection?

Add aż: Idź prosto aż do skrzyżowania i skręć w lewo przy banku. Aż do emphasizes all the way up to.

Do I need a comma before i in this sentence?

No. In Polish you normally don’t put a comma before i when it links two imperative clauses. The original punctuation is correct.

Any tips for pronouncing tricky parts like Idź, skręć, skrzyżowania, przy?

Idź: dź is a soft sound [d͡ʑ], somewhat like the j sound in English jeans but more palatal; one syllable.
skręć: ę is a nasal e; before ć it sounds close to en. ć is a soft [t͡ɕ] (like a soft tch). Approximate: skrench.
skrzyżowania: rz and ż are both pronounced like zh [ʐ]; stress is on the penultimate syllable: skrzy-żo-WA-nia.
przy: the cluster prz is [pʂ] (similar to psh), and y is the hard vowel [ɨ] (not the English i).