I have to rewrite this following sentence replacing the direct object nouns with direct object pronouns.

Elle monte l'escalier.

How would you do it???

First of all, learn the direct-object pronouns in French:

me, te, nous, vous (you don't have to really distinguish between direct or indirect-object pronouns here because in French those 4 look alike. It is 3rd person singular and plural which can cause trouble:
le, la (l' before a vowel or unsounded h ), les

The direct object is l'escalier. Knowing that it is masculine singular, it will be replaced with "le" so t he sentence is: Elle (subject) le (direct object) monte. (verb)

That will give you the word order for an affirmative sentence = subject + direct-object pronoun + verb.
Negative or interrogative sentences are a bit different.

Sra (aka Mme)

To replace the direct object nouns with direct object pronouns in the sentence "Elle monte l'escalier," follow these steps:

1. Identify the direct object noun in the sentence. In this case, the direct object noun is "l'escalier," which means "the stairs" in English.

2. Find the appropriate direct object pronoun that corresponds to the direct object noun. In this case, the correct direct object pronoun to replace "l'escalier" would be "le" because "escalier" is a masculine noun.

3. Rewrite the sentence using the direct object pronoun in place of the direct object noun. The revised sentence would be: "Elle le monte."

In summary, to rewrite the sentence, you replace the direct object noun "l'escalier" with the appropriate direct object pronoun "le," resulting in the revised sentence "Elle le monte."