Ruslagámurinn er bak við sumarbústaðinn.

Because Icelandic uses compound nouns very freely.

Ruslagámurinn can be broken down like this:

• rusl = trash, rubbish
• gámur = container / skip / dumpster
• -inn = the definite article, attached to the noun

So ruslagámurinn is literally trash-container-the.

This is very normal in Icelandic. Where English often uses multiple words, Icelandic often packs the idea into one compound word.

In Icelandic, the is usually added to the end of the noun as a suffix instead of being a separate word.

So:

• ruslagámur = a dumpster
• ruslagámurinn = the dumpster

and

• sumarbústaður = a summer house / summer cottage
• sumarbústaðinn = the summer house / summer cottage

That is one of the first big differences English speakers notice.

Er means is.

It is the present tense, singular form of vera (to be).

So:

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

In this sentence, the subject is singular (Ruslagámurinn), so er is the correct form.

Bak við means behind.

It is best learned as a fixed expression. Even though the parts can be understood separately, in a sentence like this you should treat bak við as one unit meaning behind.

So:

• bak við húsið = behind the house
• bak við bílinn = behind the car

For a learner, the safest approach is: memorize bak við as the normal phrase for behind.

Because the noun comes after við, and við takes the accusative case.

The basic dictionary form is:

• sumarbústaður = summer house

The definite singular forms are:

• sumarbústaðurinn = nominative singular definite
• sumarbústaðinn = accusative singular definite

Since bak við uses við, the noun after it appears in the accusative:

• bak við sumarbústaðinn

This is a very common Icelandic pattern: the preposition determines the case of the following noun.

Because the two nouns have different jobs in the sentence.

• Ruslagámurinn is the subject, so it is in the nominative
• sumarbústaðinn comes after the preposition við, so it is in the accusative

So the sentence shows two different cases:

• Ruslagámurinn = nominative singular definite
• sumarbústaðinn = accusative singular definite

English does not mark this very much on nouns, but Icelandic does, so this is an important thing to notice.

Yes. This is a very normal Icelandic sentence pattern:

• subject + verb + prepositional phrase

So:

• Ruslagámurinn = subject
• er = verb
• bak við sumarbústaðinn = location phrase

You can also move the location phrase to the front:

• Bak við sumarbústaðinn er ruslagámurinn.

That is also grammatical. Icelandic often allows this kind of movement, but the finite verb usually stays in the second position.

If you remove the definite article, you get an indefinite meaning:

• Ruslagámur er bak við sumarbústað.

That means roughly A dumpster is behind a summer house.

Notice that the case still matters:

• ruslagámur = nominative singular
• sumarbústað = accusative singular after við

So removing -inn does not remove case; it only removes definiteness.

A rough English-friendly pronunciation would be:

RUS-la-gow-mu-rinn er bahk vith SU-mar-boo-sta-thinn

A few useful points:

• á sounds roughly like ow in cow
• ð is like th in this
• Icelandic usually stresses the first syllable of a word

So pay special attention to:

• RUSlagámurinn
• SUmarbústaðinn

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