Сушильная машина работает.

Literally, it is drying machine:

• сушильная = drying
• машина = machine

In everyday Russian, сушильная машина is the standard way to say dryer or tumble dryer.

Because it is an adjective agreeing with машина.

• машина is feminine
• singular
• nominative case

So the adjective also has to be feminine singular nominative:

• masculine: сушильный
• feminine: сушильная
• neuter: сушильное

This kind of agreement is very important in Russian.

Both сушильная and машина are in the nominative singular.

That is because сушильная машина is the subject of the sentence — it is the thing doing the action:

• Сушильная машина = the dryer
• работает = works / is working

Because the subject is singular.

• сушильная машина = one machine
• so the verb must be third person singular

The infinitive is работать = to work
Its third person singular form is работает = works / is working

If the subject were plural, you would use работают:

• Сушильные машины работают. = The dryers are working.

It can mean either one.

Russian present tense often covers both:

• works
• is working

So Сушильная машина работает could mean:

• The dryer works (it functions)
• The dryer is working (it is currently running)

The exact meaning depends on context.

The stress is:

• суши́льная
• маши́на
• рабо́тает

A rough pronunciation guide:

• soo-SHEEL-na-ya ma-SHEE-na ra-BO-ta-yet

Stress matters in Russian, so it is good to learn words together with their stress.

Yes. Russian word order is more flexible than English word order.

The neutral, basic order is:

• Сушильная машина работает.

But you could also hear:

• Работает сушильная машина.

That version might sound more like The dryer is working with a slightly different emphasis.
Even though the order changes, the meaning stays very similar because the case endings show the grammatical roles.

Russian does not have articles.

So Сушильная машина работает can mean:

• The dryer is working
• A dryer is working

Context tells you which one is meant.

This is very normal in Russian, and learners usually just need time to get used to it.

Yes. In everyday speech, many people say сушилка.

So you may hear:

• Сушилка работает.

That is less formal and more conversational.
Сушильная машина is a fuller, more explicit version.