Szlak turystyczny zaczyna się na polanie.

Because the verb here is zaczynać się, which means to begin or to start by itself.

• Szlak zaczyna się na polanie = The trail begins in/on a clearing
• Zaczynać without się is usually used when someone begins something:
  • Zaczynam lekcję = I am starting the lesson
  • Zaczynam pracę = I am starting work

So się is an important part of the meaning here.

In this sentence, się helps make the verb intransitive, so it means begins rather than starts something.

A very common pattern in Polish is:

• X zaczyna Y = X starts Y
• Y zaczyna się = Y begins

So:

• Przewodnik zaczyna wycieczkę = The guide starts the tour
• Wycieczka zaczyna się o dziewiątej = The tour begins at nine

Here, szlak is not starting something else. The trail itself is what begins, so Polish uses zaczyna się.

Polanie is in the locative case.

That is because the preposition na often takes the locative when it means location:

• na polanie = in/on the clearing
• na stole = on the table
• na ulicy = in/on the street

The basic dictionary form is polana. Its locative singular is polanie.

So:

• polana = nominative
• na polanie = locative after na

Because Polish normally uses na with polana.

This is one of those preposition patterns you mostly have to learn as a phrase:

• na polanie = in/on a clearing
• na łące = in/on a meadow
• na plaży = on the beach

Even though English often says in a clearing, Polish uses na here. It is just the natural Polish choice.

Polana usually means a forest clearing or glade: an open grassy space surrounded by trees or in woodland.

So this sentence suggests that the tourist trail starts in that kind of open natural area, not in a town, station, or building.

That is a very good question. In Polish, adjectives often do come before the noun, but some combinations are fixed or standard as noun + adjective.

Szlak turystyczny is the normal established term for a tourist trail / hiking trail.

Compare:

• szlak turystyczny = the standard name of this kind of route
• turystyczny szlak = possible, but it sounds less like a fixed label and more descriptive or stylistically marked

So in this sentence, szlak turystyczny is simply the natural expression.

Turystyczny is an adjective agreeing with szlak.

Here is the agreement:

• szlak is masculine singular
• so the adjective must also be masculine singular nominative
• that form is turystyczny

If the noun changed, the adjective would change too:

• szlak turystyczny = masculine singular
• trasa turystyczna = feminine singular
• szlaki turystyczne = plural

This kind of adjective-noun agreement is a basic feature of Polish grammar.

Yes. Polish word order is fairly flexible because endings show the grammatical relationships.

The sentence as given is neutral:

• Szlak turystyczny zaczyna się na polanie.

But you could also say:

• Na polanie zaczyna się szlak turystyczny.

That version puts more focus on na polanie, as if answering Where does the trail begin?

So the meaning stays basically the same, but the emphasis changes.

Yes, zaczyna się is present tense.

It is used here to state a general fact:

• The tourist trail begins at a clearing

Polish often uses the present tense for descriptions, general truths, instructions, maps, and signs.

The verb here is from the imperfective pair zaczynać się.
If you wanted a future one-time event, you would usually use zacznie się:

• Koncert zacznie się o 18:00 = The concert will begin at 6:00

But for a fixed feature of a trail, zaczyna się is exactly right.

A careful pronunciation is approximately:

szlak turystyczny zaczyna się na polanie
IPA: /ʂlak turɨˈstɨt͡ʂnɨ zaˈt͡ʂɨna ɕɛ na pɔˈlaɲɛ/

A rough English-friendly guide could be:

shlak too-ri-STICH-nih za-CHI-na shyeh na po-LA-nyeh

A few useful sound notes:

• sz sounds like a harder Polish sh
• cz sounds roughly like ch in church
• się has a soft consonant sound, closer to śe than to normal English she
• Polish stress is usually on the second-to-last syllable:
  • tu-rys-TYCZ-ny
  • za-CZY-na
  • po-LA-nie

You might see od polany in some contexts, but it is not exactly the same.

• na polanie focuses on location: the trail begins at/on the clearing
• od polany focuses more on starting from that point onward

So zaczyna się na polanie is very natural when you mean the physical place where the trail starts.
Od polany is more like from the clearing and can sound more directional or boundary-based.