Smápeningarnir eru á borðinu.

Because Icelandic usually attaches the definite article the to the end of the noun instead of writing it as a separate word.

• smápeningar = small coins / small change
• smápeningarnir = the small coins / the small change

The ending -nir here is the definite article for a masculine plural noun in the nominative case.

Smápeningar usually means small coins, change, or loose change. It refers to coins rather than money in general.

So in this sentence, it most naturally means something like the coins or the loose change.

Because the subject is plural.

The verb vera = to be.
Present tense:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is
• við erum = we are
• þið eruð = you are
• þeir/þær/þau eru = they are

Since smápeningarnir is plural, the sentence uses eru = are.

Because á can take different cases depending on meaning:

• location = on something already → usually dative
• movement toward a surface = onto something → usually accusative

Here the sentence describes location: the coins are on the table.
So Icelandic uses the dative form:

• á borðinu = on the table

If you were talking about movement onto the table, you would use:

• á borðið = onto the table

For example:

• Smápeningarnir eru á borðinu. = The coins are on the table.
• Ég set smápeningana á borðið. = I put the coins onto the table.

That ending shows both case and definiteness.

The base noun is:

• borð = table

Here it appears as:

• borðinu = the table in the dative singular

So the ending reflects:

• singular
• definite
• dative
• neuter noun

This is very common in Icelandic: endings carry a lot of grammar.

It is in the nominative plural.

That is because it is the subject of the sentence:

• Smápeningarnir = the coins
• eru = are
• á borðinu = on the table

In simple statements like this, the subject is usually in the nominative case.

In this sentence, yes, it is very similar:

• Smápeningarnir = subject
• eru = verb
• á borðinu = prepositional phrase

So the structure is basically:

Subject + verb + location

However, Icelandic word order is more flexible than English because case endings show grammatical roles.

Yes. That is also grammatical.

Icelandic often allows different word orders for emphasis or style.
The version with Á borðinu first puts more focus on the location:

• Smápeningarnir eru á borðinu. = neutral
• Á borðinu eru smápeningarnir. = emphasis on on the table

English can do something similar, but Icelandic uses this kind of variation more naturally.

A rough guide is:

SMAU-peh-ning-ar-nir EH-ru au BOR-thi-nu

A few useful notes:

• á sounds roughly like ow in cow
• ð is like the th in this
• r is rolled or tapped
• Icelandic stress usually falls on the first syllable of a word

So:

• SMÁ-peningarnir
• E-ru
• Á
• BOR-ðinu

Very often, yes.

Instead of a separate word like English the, Icelandic usually adds the definite article as a suffix:

• borð = table

• borðið = the table

• smápeningar = coins / change
• smápeningarnir = the coins / the change

There are a few situations where a separate demonstrative-like word may appear, but for ordinary definite nouns, the attached article is the normal pattern.

Yes. In Icelandic, smápeningar is grammatically plural.

English often says change as an uncountable noun, but Icelandic commonly uses this plural noun to refer to small coins or loose change. So even if the English translation is the change is on the table, Icelandic may still use a plural form:

• Smápeningarnir eru ... = literally the small coins are ...

That is a normal difference between the two languages.