Learn Hardcore Turkish: Patika yağmur yağınca kaygan oluyor. - The trail becomes slippery when it rains.

patika means trail or path. Turkish has no articles like a or the. Definiteness or indefiniteness is understood from context. If you want to say “a trail” explicitly, you add bir, e.g. bir patika.

How does yağmur yağınca mean “when it rains”? Where is the word “when” in Turkish?

Turkish uses the suffix -(y)ınca (also -ince, -unca, -ünce by vowel harmony) to express when, once, or as soon as. You attach it directly to the verb stem. Here:
• yağmur (rain)
• yağ- (to fall/rain)
• -ınca (when/once)
→ yağmur yağınca = “when it rains.”

Could I use yağmur yağdığında instead of yağmur yağınca?

Yes. yağmur yağdığında is formed from the past-tense stem yağdı- plus the time clause suffix -ğında (“when the rain has fallen”). It also means “when it rains,” though it’s a bit more formal or emphatic than the shorter -ınca form.

Why is oluyor used after kaygan, and what does kaygan oluyor mean?

oluyor is the 3rd person singular present of olmak, which here means to become or to get.
• kaygan oluyor means “it becomes slippery” or “it gets slippery.”
Using [adjective] + olmak/oluyor is a common way in Turkish to express a change of state or a condition.

Could we use kayganlaşmak instead of kaygan olmak?

Yes. kayganlaşmak (“to become slippery”) uses the verb-forming suffix -laşmak, which also indicates “to turn into/become.” So you could say:
Patika yağmur yağınca kayganlaşıyor.
Both kaygan oluyor and kayganlaşıyor are correct; the first is very common in everyday speech.

Why isn’t there an explicit subject pronoun like “it” for oluyor?

Turkish typically drops subject pronouns when they are clear from the verb ending. oluyor is marked for 3rd person singular, so the implicit subject “it” is understood without being stated.

Can the word order change? For example, is Yağmur yağınca patika kaygan oluyor also correct?

Yes. Turkish allows relatively flexible word order. You can place the time clause yağmur yağınca at the beginning, middle, or end to shift emphasis. All of these communicate essentially the same idea.

Should I use a comma between the clauses?

In Turkish, commas often separate clauses for clarity, so you might see:
Patika, yağmur yağınca, kaygan oluyor.
However, in simple sentences like this, commas are optional: Patika yağmur yağınca kaygan oluyor is perfectly clear without them.