Trampólínið er blautt eftir rigninguna.

Because Icelandic usually puts the definite article on the end of the noun instead of using a separate word like the.

• trampólín = trampoline
• trampólínið = the trampoline

The ending -ið is the neuter singular definite article here.

So:

• Trampólín er blautt = A trampoline is wet / Trampoline is wet (depending on context)
• Trampólínið er blautt = The trampoline is wet

Because the adjective has to agree with the noun it describes.

The noun trampólín is:

• neuter
• singular

So the adjective blautur (wet) must also be in the neuter singular form:

• blautur = masculine
• blaut = feminine
• blautt = neuter

Since trampólínið is neuter, Icelandic uses blautt.

This happens even though blautt comes after er. In Icelandic, predicate adjectives still agree with the subject:

• Maðurinn er blautur = The man is wet
• Konan er blaut = The woman is wet
• Trampólínið er blautt = The trampoline is wet

Er is the present tense, third-person singular form of the verb vera (to be).

So here:

• Trampólínið er blautt = The trampoline is wet

Other common forms of vera include:

• ég er = I am
• þú ert = you are
• hann/hún/það er = he/she/it is
• við erum = we are

Rigninguna means the rain in a specific sense, with the definite article attached.

Breakdown:

• rigning = rain
• rigningin = the rain (dictionary-style nominative form)
• rigninguna = a case form of the rain

In this sentence, eftir requires a particular case here, so rigningin changes to rigninguna.

So this is not a random change: it is the noun rigningin being declined.

Because eftir takes the accusative case when it means after in time.

Here it means after the rain, so the noun after eftir must be accusative:

• nominative: rigningin
• accusative: rigninguna

So:

• eftir rigninguna = after the rain

This is a very common thing in Icelandic: prepositions often control the case of the noun that follows them.

Literally, it means after the rain, so it is mainly temporal: the trampoline is wet following the rain.

In natural use, though, it also strongly suggests the rain is the reason it is wet. So in English, the idea is close to:

• The trampoline is wet after the rain
• The trampoline is wet from the rain

If you wanted to say because of the rain more directly, Icelandic could use a different expression, such as vegna rigningarinnar.

It is a loanword, adapted to Icelandic spelling and grammar.

That is very common in Icelandic, especially for modern objects. Even borrowed nouns still behave like Icelandic nouns grammatically, which is why you get forms like:

• trampólín
• trampólínið

So even though the word is borrowed, it still takes Icelandic endings and agrees with Icelandic adjectives.

A rough pronunciation guide for an English speaker is:

Trampólínið er blautt eftir rigninguna
≈ trahm-POH-lee-nith er blöyt ehp-tir RIG-ning-oo-na

A few notes:

• í is like ee in see
• ð in -ið is a soft voiced sound, often like th in this, though in fast speech it can be weaker
• au in blautt is pronounced somewhat like öy
• the stress in Icelandic usually falls on the first syllable of each word

This is only an approximation, but it helps as a starting point.

Yes, Icelandic allows some flexibility in word order.

For example, you could also say:

Eftir rigninguna er trampólínið blautt.

That still means The trampoline is wet after the rain, but now the time phrase is emphasized a bit more.

One important thing to notice is that Icelandic often keeps the finite verb in the second position:

• Trampólínið er blautt eftir rigninguna
• Eftir rigninguna er trampólínið blautt

So when you move eftir rigninguna to the front, er still comes next.

Sometimes, yes, but blautur is the more natural everyday word for something that is physically wet.

• blautur / blautt = wet
• votur / vott can also mean wet, but it is often less common in casual speech for many situations

For a wet trampoline, blautt is a very natural choice.

The main dictionary forms are:

• trampólínið → trampólín = trampoline
• er → vera = to be
• blautt → blautur = wet
• eftir → eftir = after
• rigninguna → rigning = rain

This is useful because Icelandic words often appear in changed forms in real sentences, so learning to recognize the dictionary form helps a lot.