A dolgozóasztal a munkaállomás mellett van.

Because a is the Hungarian definite article, meaning the.

So:

• a dolgozóasztal = the desk
• a munkaállomás mellett = next to the workstation

Hungarian normally uses the definite article before definite nouns much like English does. The form is:

• a before a consonant
• az before a vowel

So here both nouns begin with consonants, so both take a.

Yes, it is one word, and it is a compound noun.

It is made up of:

• dolgozó = working / work-related
• asztal = table

Together, dolgozóasztal means something like work table or desk.

A native English speaker may expect two separate words, but Hungarian very often builds new nouns by combining words into a single compound.

Also, in everyday Hungarian, íróasztal is a very common word for desk, so a learner might encounter both.

It is also a compound noun:

• munka = work
• állomás = station

So munkaállomás literally means workstation.

This is a very typical Hungarian pattern: two nouns combine into one longer noun. English often does something similar, but Hungarian usually writes these as one word.

Because mellett is a postposition, not a preposition.

English uses prepositions:

• next to the workstation

Hungarian often uses postpositions:

• a munkaállomás mellett
• literally: the workstation next-to

So instead of coming before the noun phrase, the word expressing the relationship comes after it.

This is very normal in Hungarian. Other common postpositions are things like:

• előtt = in front of
• mögött = behind
• alatt = under

Because with most postpositions like mellett, the noun stays in its basic form.

So you say:

• a munkaállomás mellett

not something like a munkaállomást mellett

In other words, mellett itself carries the meaning next to / beside, so the noun does not need an extra case ending here.

That is something English speakers often need to get used to: sometimes Hungarian uses a suffix, and sometimes it uses a separate postposition.

That is a very common and important question.

Hungarian often leaves out van in the present tense when you are simply saying that something is something or has a quality:

• Az asztal nagy. = The table is big.
• Ő tanár. = He/She is a teacher.

But in location sentences, Hungarian normally does use van:

• A könyv az asztalon van. = The book is on the table.
• A dolgozóasztal a munkaállomás mellett van. = The desk is next to the workstation.

So here van is necessary because the sentence tells you where something is.

This is a natural neutral word order in Hungarian.

The sentence is structured like this:

• A dolgozóasztal = topic, what we are talking about
• a munkaállomás mellett van = what we say about it

Placing van at the end is very common in simple locational sentences.

Hungarian word order is more flexible than English word order, but the different orders can change emphasis. In this sentence, the order sounds neutral and natural.

Yes. Hungarian word order is flexible, so you could also say:

• A munkaállomás mellett van a dolgozóasztal.

This still means essentially the same thing, but the emphasis is a bit different. It puts more attention on the location first, almost like:

• Next to the workstation, there is the desk.

The original sentence is the more straightforward choice if the topic is the desk.

Usually it is a very good match for next to or beside.

So:

• a munkaállomás mellett = next to the workstation / beside the workstation

However, like many words, exact usage depends on context. In most everyday physical-location sentences, mellett is the right choice for something positioned beside something else.

Then you would usually use egy for a/an:

• Egy dolgozóasztal a munkaállomás mellett van.

That means A desk is next to the workstation.

So:

• a dolgozóasztal = the desk
• egy dolgozóasztal = a desk

English speakers should be careful here, because Hungarian articles do not always match English perfectly in every situation, but in a simple sentence like this, that is the basic difference.

A rough English-friendly guide would be:

• A = short aw
• dolgozóasztal ≈ DOL-go-zoh-aws-tawl
• a = aw
• munkaállomás ≈ MOON-kaw-aal-loh-maash
• mellett ≈ MEL-lett
• van = vawn

A few useful pronunciation points:

• Stress is normally on the first syllable of each word.
• á is longer than a.
• ó is a long o sound.
• Double consonants like ll and tt are pronounced longer or more firmly than single ones.

You do not need to sound perfectly native right away; getting the first-syllable stress and the vowels roughly right will already help a lot.

Yes. It is a very typical pattern for stating location:

• [definite noun] + [place expression] + van

For example:

• A szék az asztal mellett van. = The chair is next to the table.
• A számítógép az ablak előtt van. = The computer is in front of the window.

So this sentence is useful as a model. If you understand it, you can build many similar location sentences in Hungarian.