Learn German: Sucht ihr den Stift? - Are you looking for the pen?

Stift (pen) is a masculine noun, so its basic 'dictionary' article is der. However, in this sentence, the pen is the direct object—the thing being looked for. This puts it in the accusative case, and the masculine der changes to den in the accusative.

The English translation says 'looking for', but I don't see a German word for 'for'. Why is that?

The German verb suchen means 'to look for' or 'to search for'. The idea of 'for' is already built into the verb itself, so you just use suchen directly followed by the object you are looking for. You don't need to add a translation for 'for' like für.

Why does the sentence use ihr for 'you'?

ihr is the informal plural 'you' (think 'you all' or 'you guys'). The speaker is asking two or more people. If they were asking just one person informally, they would use du and the verb would change: Suchst du den Stift?.

Why does the sentence start with the verb Sucht?

To ask a yes/no question in German, you just move the conjugated verb to the very front of the sentence. The statement 'You all are looking for the pen' is Ihr sucht den Stift. Moving the verb to the start makes it a question: Sucht ihr den Stift?.