Learn Turkish: Çadırı kurduktan sonra yeşil bereyi bulamadım. - After setting up the tent, I could not find the green beanie.

To say "after doing [verb]", Turkish adds -dIktan (or its vowel/consonant harmony variants) + sonra to the verb root. Here, kur- (to set up) becomes kurduktan sonra. This is actually the past participle -dUk combined with the ablative case -tAn ("from").

Why do both çadır and bere have accusative suffixes here?

They are both specific direct objects in their respective clauses ("the tent" and "the green beanie"). Çadır (tent) gets -ı to become çadırı because it is the object of the verb setting up. Bere (beanie) gets -yi (using the buffer y) because it is the object of the verb finding.

What is the difference between bulmadım and bulamadım?

Bulmadım simply means "I didn't find". The verb in this sentence is bulamadım, which includes the potential negative suffix -ama (the ability vowel -a- plus the negative -ma-). This changes the meaning to "I couldn't find" or "I was unable to find".

Why is the suffix -tan used in kurduktan instead of the usual -dan?