Если на столе пятно, лучше вытереть его тряпкой.

Because на столе expresses location: the stain is on the table.

With на:

• на + accusative usually means motion onto something
• на + prepositional usually means location on something

So:

• положить книгу на стол = put the book onto the table
• книга на столе = the book is on the table

Here we are describing where the stain is, so Russian uses the prepositional case: на столе.

Because пятно is the thing that exists/is located there: there is a stain on the table.

In Russian, expressions like на столе пятно literally work like on the table [is] a stain, where пятно is the subject, so it stays in the nominative.

Even though English uses there is, Russian often simply states the location first and then the noun:

• На столе книга = There is a book on the table
• На столе пятно = There is a stain on the table

In the present tense, Russian usually omits to be.

So English If there is a stain on the table becomes simply:

• Если на столе пятно

You could say Если на столе есть пятно, and that is grammatical, but есть is often unnecessary here. Without есть, the sentence sounds natural and concise.

Лучше means better, but in sentences like this it works as an impersonal predicate: it is better to...

So:

• лучше вытереть = it is better to wipe
• more naturally in English: you’d better wipe / it’s better to wipe

There is no explicit subject like я, ты, or мы. It is general advice.

Because вытереть is perfective, and here the sentence recommends a single completed action: wiping the stain off.

• вытирать = imperfective, process/repeated action
• вытереть = perfective, complete the action

Since the idea is if there’s a stain, remove it, the completed result matters, so вытереть is the natural choice.

Russian often uses impersonal constructions for general advice.

So instead of saying:

• you should wipe it Russian can say:
• лучше вытереть его тряпкой literally, better to wipe it with a cloth

This avoids specifying who should do it. It sounds neutral and natural.

Его is correct because here the pronoun is the direct object of вытереть.

• пятно is neuter singular
• the accusative form of the pronoun referring to it is его

Compare:

• Оно на столе. = It is on the table.
  Here оно is the subject.
• Я вытер его. = I wiped it.
  Here его is the object.

So in this sentence, его means it in the sense of wipe it.

Because it expresses the tool used to do the action: with a cloth/rag.

Russian often uses the instrumental case to show means or instrument, especially when English uses with:

• писать ручкой = write with a pen
• резать ножом = cut with a knife
• вытереть тряпкой = wipe with a cloth

So тряпкой is instrumental singular of тряпка.

Because short pronoun objects like его often come earlier in the sentence, before heavier information like тряпкой.

So:

• вытереть его тряпкой sounds natural and neutral

Russian word order is flexible, so вытереть тряпкой его is not impossible in a special context, but it would sound marked or emphatic. In a normal sentence, его usually comes first.

Yes, absolutely.

That version is also correct:

• Если на столе есть пятно, лучше вытереть его тряпкой.

Adding есть makes the existence slightly more explicit. But in everyday Russian, it is often omitted in present-tense existential sentences, so the original version sounds very natural.

Because Если на столе пятно is a subordinate clause introduced by если (if), and it is followed by the main clause:

• лучше вытереть его тряпкой

Russian punctuation requires a comma between those parts:

• Если ..., ...

So the comma is standard and necessary here.