De koekenpan staat naast het vergiet op het aanrecht.

In Dutch, you often use a position verb for the location of an object:

• staan = to stand
• liggen = to lie
• zitten = to be situated / to be in
• hangen = to hang

A koekenpan is treated as something that is upright or resting in a standing position here, so Dutch uses staat.

So:

• De koekenpan staat naast het vergiet. = The frying pan is next to the colander.

English usually just says is, but Dutch prefers a more specific verb when talking about where things are.

Dutch nouns have grammatical gender, and singular nouns usually take either:

• de
• het

In this sentence:

• de koekenpan
• het vergiet
• het aanrecht

There is no simple rule that always tells you which article a noun takes, so this often has to be learned with the noun itself.

A useful habit is to learn nouns as a full unit:

• de koekenpan
• het vergiet
• het aanrecht

Naast means next to or beside.

It is a preposition, so it comes before the noun phrase:

• naast het vergiet = next to the colander

This works much like English:

• naast de deur = next to the door
• naast het huis = next to the house

So in your sentence, de koekenpan is located naast het vergiet.

In normal interpretation, op het aanrecht gives the location of the whole situation: the frying pan is next to the colander, and this is happening on the countertop.

So the most natural meaning is:

• the frying pan is on the countertop
• the colander is also on the countertop
• the frying pan is next to the colander

Dutch often leaves this kind of relationship slightly implicit, just as English can.

Yes. That is also natural Dutch.

Both versions are possible:

• De koekenpan staat naast het vergiet op het aanrecht.
• De koekenpan staat op het aanrecht naast het vergiet.

The difference is mostly one of emphasis and flow.

• naast het vergiet first: emphasizes what it is next to
• op het aanrecht first: emphasizes where it is

Both are grammatically fine.

Because modern Dutch has very little case marking in ordinary usage.

So after prepositions like naast and op, the article usually stays the same:

• naast het vergiet
• op het aanrecht

Unlike German, Dutch does not normally change het into a different article form in this kind of sentence.

Yes. Dutch very often forms compound nouns by writing them as one word.

So:

• koekenpan = frying pan
• literally something like cake/pancake pan historically, but as a normal word it just means frying pan

This one-word spelling is very common in Dutch:

• huisdeur = house door / front door
• tafelkleed = tablecloth
• wasmachine = washing machine

For English speakers, Dutch compounds often look long, but they are completely normal.

Dutch main clauses usually follow the V2 rule: the finite verb comes in the second position.

Here the sentence begins with the subject:

• De koekenpan = position 1
• staat = position 2

Then the rest follows:

• naast het vergiet op het aanrecht

So the pattern is:

• Subject + finite verb + rest

If you move something else to the front, the verb still stays second:

• Op het aanrecht staat de koekenpan naast het vergiet.

That is a very important Dutch word-order pattern.

Sometimes, yes, depending on how you imagine the frying pan.

Dutch chooses location verbs based on the perceived position of the object:

• staat if it is considered upright or standing
• ligt if it is lying flat

A frying pan on a counter is often said to staan, but in some contexts a speaker might also say ligt, especially if they are thinking of it as lying flat.

So:

• De koekenpan staat op het aanrecht.
• De koekenpan ligt op het aanrecht.

Both can occur, but staat in your sentence is perfectly normal.

A rough English-friendly guide:

• vergiet: the second part sounds roughly like GHEET, with a Dutch g/ch sound that English does not really have
• aanrecht: roughly AHN-rekht, again with that Dutch throat sound in recht

A few helpful notes:

• aa is a long a
• ie sounds like ee in see
• ch/g in many Dutch accents is a throat/fricative sound, not an English g

Exact pronunciation depends somewhat on accent, but those rough guides will help.

Yes. Het aanrecht refers to the kitchen counter / countertop, especially the work surface in a kitchen.

So op het aanrecht means:

• on the countertop
• on the kitchen counter

That is the normal everyday meaning here.