Learn Russian: Я хочу починить туфлю, мне нужен клей.

When you need a specific object, Russian literally phrases it as "to me, the object is necessary." The word for "necessary" acts like a short adjective and must match the gender and number of the thing you need. Since клей (glue) is a masculine singular noun, it takes the masculine form нужен.

Why does the second part of the sentence start with мне instead of я?

With words expressing personal necessity like нужен, the person experiencing the need must be in the dative case. Мне is the dative form of я. The literal structure of this clause is "To me, glue is necessary."

What is the dictionary form of туфлю?

The dictionary form is туфля, which is a feminine noun meaning "shoe". In this sentence, it takes the accusative case ending -ю because it is the direct object receiving the action of being fixed.

Why use the perfective verb починить instead of the imperfective чинить?

You use the perfective verb починить because you are focusing on the successful completion of a single, specific action. You want to achieve the result of getting this particular shoe fixed, rather than just describing the ongoing process of fixing things.

The English translation says "my shoe", but there is no word for "my" in the Russian sentence. Why?