Learn Spanish (Latin America): Encuadernamos los libros con cuero.

Yes! The verb encuadernar (to bind a book) is formed from the root of cuaderno by adding the prefix en- and the verb suffix -ar. You will see this word-building pattern often in Spanish, such as turning botella (bottle) into embotellar (to bottle).

Is encuadernamos in the present or the past tense here?

It can be either! For regular -ar (and -ir) verbs, the nosotros form is identical in the present tense and the preterite (simple past). You would need more context to know for sure if the sentence translates to "we bind" or "we bound."

Why doesn't cuero need a definite article here, like con el cuero?

When referring to an uncountable material or substance in a general sense, Spanish drops the article, just like English. If you said con el cuero, it would mean "with the leather," referring to a specific piece of leather that you and the listener already know about.

Could we say de cuero instead of con cuero?