Retkeilyreitti alkaa opasteen vierestä.

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

• retkeily = hiking, trekking, outdoor excursion activity
• reitti = route, trail, path

So retkeilyreitti literally means something like hiking-route, which English would usually express as hiking trail or hiking route.

Because it is the subject of the sentence, and the subject is normally in the nominative singular in a sentence like this.

So:

• retkeilyreitti = nominative singular
• it is the thing that begins

That is why you do not see an extra case ending on it here.

alkaa is the 3rd person singular present tense of the verb alkaa, meaning to begin or to start.

It matches the singular subject retkeilyreitti.

A few forms of the verb are:

• minä alan = I begin
• sinä alat = you begin
• hän alkaa = he/she begins
• reitti alkaa = the route begins

So in this sentence, retkeilyreitti alkaa means the trail begins.

Because opasteen is the genitive singular of opaste.

The word vierestä functions as a postposition here, and postpositions in Finnish commonly require the noun before them to be in the genitive.

So:

• opaste = a sign, guide sign, marker
• opasteen = of the sign / the sign’s

In this structure:

• opasteen vierestä = from beside the sign

vierestä means from beside, from next to, or from the side of.

It expresses movement or origin from a nearby location.

So:

• jonkin vieressä = beside something
• jonkin vierestä = from beside something
• jonkin viereen = to beside something / up next to something

In this sentence, the trail begins from beside the sign, so vierestä is the correct form.

Because alkaa refers to a starting point, not just a location.

• vieressä = beside / next to (static location)
• vierestä = from beside / from next to (starting point or movement away from a place)

Compare:

• Retkeilyreitti on opasteen vieressä. = The hiking trail is beside the sign.
• Retkeilyreitti alkaa opasteen vierestä. = The hiking trail begins from beside the sign.

So vierestä fits the idea of where the trail starts.

opaste is a general word for a sign that gives directions or guidance.

Depending on context, it could be:

• a guide sign
• a directional sign
• a trail marker
• an information sign

In a hiking context, it usually suggests some kind of trail sign or wayfinding sign.

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

The sentence:

• Retkeilyreitti alkaa opasteen vierestä.

is a neutral way to say it.

But you could also say:

• Opasteen vierestä alkaa retkeilyreitti.

That still means the same thing, but it puts more emphasis on the location from beside the sign.

So the case endings do a lot of the grammatical work, which makes word order freer.

Because Finnish does not normally use articles like English does.

So retkeilyreitti can mean:

• a hiking trail
• the hiking trail

and opasteen can correspond to:

• of a sign
• of the sign

The exact English choice depends on context. Finnish usually leaves that unstated unless something else makes it specific.

In practice, you should learn vieressä, vierestä, and viereen as location words that behave like postpositions in expressions such as:

• talon vieressä = beside the house
• talon vierestä = from beside the house
• talon viereen = to beside the house

The important pattern for a learner is:

• the noun before them is usually in the genitive
• the ending on vier- shows the location relationship:
  • -ssä = in/at
  • -stä = from
  • -en = to

So even if you do not focus on the full grammatical classification yet, the usable pattern is very consistent.