Learn Spanish (Latin America): Necesito un lápiz para escribir la carta.

You would use the demonstrative adjectives from this lesson! Because lápiz is a masculine word, you use este, and because carta is feminine, you use esta. The sentence becomes: Necesito este lápiz para escribir esta carta.

Why is escribir not conjugated here?

In Spanish, when a verb immediately follows a preposition like para (which means 'in order to' here), it stays in its full dictionary form, called the infinitive. So 'in order to write' is simply para escribir.

Why do we use para instead of por to mean 'to'?

A great rule to remember is that para is used for goals or purposes. When you can replace the English word 'to' with 'in order to', you almost always need para in Spanish. Here, you need a pencil in order to write the letter.

I noticed lápiz ends in a Z. How would I say 'some pencils' if I needed more than one?

Nouns that end in a Z change the Z to a C before adding -es to become plural. So, 'some pencils' translates to unos lápices.