A látásvizsgáló tábla a falon van.

Literally, it means something like vision-testing board/chart:

• látás = sight, vision
• vizsgáló = examining, testing
• tábla = board, chart, sign, table, depending on context

So in natural English, látásvizsgáló tábla is best understood as eye chart.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Here:

• látásvizsgáló starts with l, a consonant, so a látásvizsgáló tábla
• falon starts with f, a consonant, so a falon

If the next word began with a vowel, you would use az instead.

Because a / az means the, while egy means a / an.

In this sentence, the chart and the wall are understood as definite, specific things:

• A látásvizsgáló tábla = the eye chart
• a falon = on the wall

If you said egy látásvizsgáló tábla, that would mean an eye chart, not the eye chart.

falon means on the wall.

It is made from:

• fal = wall
• -on = a case ending meaning on a surface

So Hungarian often uses an ending where English uses a separate preposition.

This ending is called the superessive case. It usually means on something:

• asztalon = on the table
• polcon = on the shelf
• falon = on the wall

Because falon shows a location, while falra shows movement toward a surface.

• a falon van = it is on the wall
• a falra teszi = he/she puts it onto the wall

So:

• -on / -en / -ön = static location, on
• -ra / -re = motion onto something, onto

This is a very important distinction in Hungarian.

That is a very common and very good question.

Hungarian often leaves out van in the present tense when the sentence simply says what something is:

• A tábla nagy. = The chart is big.
• A férfi orvos. = The man is a doctor.

But when you talk about where something is, Hungarian normally uses van:

• A látásvizsgáló tábla a falon van. = The eye chart is on the wall.

So in short:

• identity / description in present tense: often no van
• location / existence: usually van

No, Hungarian word order is flexible, but different orders change the emphasis.

The sentence as given is a neutral way to say it:

• A látásvizsgáló tábla a falon van. = The eye chart is on the wall.

Other orders are possible:

• A falon van a látásvizsgáló tábla. = The eye chart is on the wall.
  This can put more focus on where it is.

• A látásvizsgáló tábla van a falon. = It is the eye chart that is on the wall.
  This sounds more contrastive, as if distinguishing it from something else.

So the original sentence is the most neutral beginner-friendly version.

In this sentence, látásvizsgáló functions as a modifier of tábla, so it works somewhat like an adjective in English.

It is built from smaller parts:

• látás = vision
• vizsgáló = examining / testing

Together, látásvizsgáló means vision-testing.

Hungarian often builds long compound words like this. That is very normal. So although it may look intimidating, it is just a compact way of saying vision-testing chart.

A rough pronunciation guide is:

aw LAA-taash-vizh-GAA-loh TAAB-law aw FAW-lon vawn

A few useful sound notes:

• á is long, like the a in father
• sz is pronounced like English s
• zs is like the s in measure
• ó is a long o
• a in Hungarian is not exactly the English a; it is a short open sound

Stress in Hungarian normally falls on the first syllable of each word:

• LÁtásvizsgáló
• TÁBla
• FAlon
• VAN

Yes. tábla has a fairly broad meaning, and the exact translation depends on context.

It can mean things like:

• board
• sign
• plaque
• chart
• table

In látásvizsgáló tábla, the natural English meaning is eye chart, not just board.

So this is a good example of how you should translate the whole phrase naturally, not word-for-word only.

Normally, no. The natural standard form is:

A látásvizsgáló tábla a falon van.

Hungarian uses the article with the noun phrase here, just as English says on the wall, not just on wall.

Leaving out a would sound ungrammatical or very unnatural in ordinary speech.