Het netwerk werkt goed.

Because netwerk is a het-word (a neuter noun).

In Dutch, singular nouns normally take either de or het:

• de tafel
• het huis
• het netwerk

You usually need to learn the article together with the noun. A useful extra clue: in the plural, it becomes de netwerken.

Werkt comes from the verb werken, which means to work or to function.

Here it is in the present tense, with a third-person singular subject: het netwerk.

Basic present-tense forms:

• ik werk = I work
• jij werkt = you work
• hij/zij/het werkt = he/she/it works
• wij werken = we work

So:

• het netwerk werkt = the network works / is working

Because goed is the word used for well/good in the sense of functioning properly.

• Het netwerk werkt goed = the network works well

Wel usually does not mean well. It often means something like:

• indeed
• actually
• do
• in fact

Compare:

• Het netwerk werkt goed. = The network works well.
• Het netwerk werkt wel. = The network does work. / The network works, actually.

So wel would sound like a contrast or correction, not a description of quality.

Here it is functioning as an adverb: it describes how the network works.

That is important because Dutch often uses goed where English would use well.

So:

• Het netwerk werkt goed. = The network works well

Compare:

• een goed netwerk = a good network
  Here goed is an adjective describing the noun netwerk.

One thing that can confuse English speakers: Dutch often uses the same form for adjective and adverb, while English often changes good to well.

Because goed is not directly describing the noun netwerk here. It is describing the verb werkt.

• het netwerk werkt goed → goed describes works
• het goede netwerk → goede describes network

When an adjective comes before a noun, it often gets an -e ending:

• het goede netwerk
• een goed netwerk

But in your sentence, goed is not an adjective before the noun, so it stays goed.

In a simple Dutch main clause, the finite verb usually comes in second position.

So the pattern here is:

• Het netwerk = subject
• werkt = finite verb
• goed = adverb

This gives:

• Het netwerk werkt goed.

You can see the same rule if another element comes first:

• Vandaag werkt het netwerk goed.

The verb werkt is still in second position.

A useful comparison:

• main clause: Het netwerk werkt goed.
• subordinate clause: Ik denk dat het netwerk goed werkt.

In the subordinate clause, werkt moves later.

They are similar, but not the same.

• Het netwerk werkt goed = the network functions well
• Het netwerk is goed = the network is good

The first sentence is about performance/functioning.
The second is a more general judgment about the network.

If you are talking about technology and you mean that it is operating properly, werkt goed is usually the more natural choice.

Netwerk is a broad word. It can mean different kinds of networks depending on context, such as:

• a computer network
• a Wi-Fi/network connection
• a professional network
• a social network

In many everyday modern contexts, especially with a sentence like Het netwerk werkt goed, people will often understand it as a technical/computer/network connection meaning.

A rough learner-friendly guide:

• het → roughly het with a short e
• netwerk → roughly NET-verk
• werkt → roughly verkt
• goed → starts with a guttural Dutch g/ch sound, not the English g

A few pronunciation notes:

• The Dutch w is usually closer to an English v than an English w.
• In netwerk and werkt, that w may sound more like v to English ears.
• The g in goed is one of the classic Dutch sounds; depending on accent, it can sound harsher or softer.
• In normal speech, het is often reduced, closer to ut.

So a very rough approximation could be:

ut NET-verk verkt khoot

That is only approximate, but it can help you get started.

Yes, often you can.

• Het netwerk werkt goed.
• Het netwerk functioneert goed.

Both are correct, but werkt goed is more everyday and common.
Functioneert goed sounds a bit more formal or technical.

So if you want the most natural everyday sentence, Het netwerk werkt goed is an excellent choice.