Learn Turkish: İtfaiye geldikten sonra yangını söndürebildik. - After the fire brigade arrived, we managed to put out the fire.

It starts with the verb root söndür (put out / extinguish). Then we add the ability suffix -ebil (can / able to), followed by the past tense suffix -di (was / did), and finally the personal ending -k (we). Altogether, söndür-ebil-di-k means "we were able to put out" or "we managed to put out".

Why does the sentence use geldikten sonra instead of just "geldi sonra"?

In English, you can just say "after the fire brigade arrived." But in Turkish, you can't just stick sonra (after) next to a regular past-tense verb. To say "after doing [action]", you must attach the special suffix -DIkten (or -tıktan, etc.) to the verb root before the word sonra. Here, gel (come) becomes geldikten sonra to mean "after arriving."

Why is there an -ı at the end of yangını?

The base word for fire is yangın. Because they managed to put out a specific fire that was already known or mentioned, it takes the accusative case (the specific direct object marker). That turns yangın into yangını.

I've seen the verb sönmek before. What is the difference between sönmek and söndürmek?