Meine Schwester legt den Topflappen neben den Herd.

Meine Schwester is the subject of the sentence, so it is in the nominative case.

• Schwester is a feminine noun: die Schwester
• In the nominative feminine, mein becomes meine

So:

• meine Schwester = my sister as the subject

You would see other forms in other cases, for example:

• meiner Schwester = dative/genitive contexts
• meine Schwester = nominative or accusative feminine

In this sentence, she is the one doing the action, so nominative is needed.

Legt is the 3rd person singular present-tense form of legen.

The subject is meine Schwester, which is equivalent to she, so the verb must match sie legt.

Present-tense forms of legen:

• ich lege
• du legst
• er/sie/es legt
• wir legen
• ihr legt
• sie/Sie legen

So Meine Schwester legt ... means My sister puts/lays ...

This is a very common German question.

• legen = to lay / to put something somewhere
  
  • it usually takes a direct object
  • it describes causing something to be in a lying position
• liegen = to lie / to be lying
  • it does not take a direct object in this meaning
  • it describes the state/location of something

Compare:

• Meine Schwester legt den Topflappen neben den Herd.
  My sister puts the potholder next to the stove.
• Der Topflappen liegt neben dem Herd.
  The potholder is lying next to the stove.

So in your sentence, there is an action of moving the potholder into position, so legt is correct.

Den Topflappen is the direct object, so it is in the accusative case.

The noun is:

• der Topflappen = the potholder

Since Topflappen is masculine, the definite article changes like this:

• nominative: der Topflappen
• accusative: den Topflappen

Because your sister is doing something to the potholder—she is placing it somewhere—it becomes the accusative object.

Topflappen is a German noun meaning potholder or sometimes hot pad, depending on context.

It is made from:

• Topf = pot
• Lappen = cloth/rag

So the word literally suggests something like a pot cloth.

German often builds nouns by combining smaller words into one larger noun.

This is about two-way prepositions.

Neben can take either:

• accusative when there is movement toward a destination
• dative when there is location only

In your sentence, the potholder is being placed next to the stove, so there is movement to that position. That is why German uses the accusative:

• neben den Herd = to next to the stove

If you were only describing where it already is, you would use dative:

• Der Topflappen liegt neben dem Herd.
  The potholder is lying next to the stove.

So:

• Wohin? (where to?) → accusative
• Wo? (where?) → dative

Herd is a masculine noun:

• der Herd = the stove / cooker

Because neben is using the accusative here, der changes to den:

• nominative: der Herd
• accusative: den Herd
• dative: dem Herd

That is why the sentence has neben den Herd.

In many everyday sentences, legen is best translated as put.

More literally, it often has the sense of lay—especially when something ends up in a flat or lying position.

So in this sentence:

• legt den Topflappen neben den Herd

can be understood as:

• puts the potholder next to the stove
• or more literally, lays the potholder next to the stove

In normal English, puts is usually the most natural translation.

In German, all nouns are capitalized.

So:

• Schwester
• Topflappen
• Herd

all begin with capital letters because they are nouns.

Words like meine, legt, and neben are not nouns, so they are not capitalized unless they start the sentence.

This is one of the most noticeable spelling differences between German and English.

This is normal German main-clause word order.

The sentence is:

• Meine Schwester = subject
• legt = verb
• den Topflappen = object
• neben den Herd = prepositional phrase

So the pattern is basically:

Subject + verb + object + place/direction

That is very common in German main clauses.

The important rule is that in a normal main clause, the conjugated verb is in the second position:

• Meine Schwester legt den Topflappen neben den Herd.

You could also move another element to the front for emphasis, but then the verb still stays second:

• Den Topflappen legt meine Schwester neben den Herd.
• Neben den Herd legt meine Schwester den Topflappen.

Those are less neutral, but grammatically possible.

Usually, no—not in the same way.

German often distinguishes placement verbs more specifically than English:

• legen = put something so that it lies
• stellen = put/set something so that it stands upright
• setzen = set something into a sitting position

A Topflappen is something flat and soft, so legen is the natural verb.

Using stellen would sound odd because a potholder does not normally stand.

Then German would usually switch from the action verb legen to the state verb liegen, and from accusative to dative after neben.

So you would get:

• Der Topflappen liegt neben dem Herd.

Changes:

• legt → liegt
• den Herd → dem Herd
• the subject becomes Der Topflappen

That sentence means the potholder is already lying there, not being moved there.