Ég þarf að kaupa sjampó í búðinni á horninu.

In this sentence, að is the infinitive marker, similar to English to in I need to buy.

• þarf = need
• að kaupa = to buy

So Ég þarf að kaupa sjampó literally matches I need to buy shampoo.

A useful pattern to remember is:

• þurfa að + infinitive = to need to do something

Examples:

• Ég þarf að sofa. = I need to sleep.
• Við þurfum að fara. = We need to go.

Kaupa is the infinitive, the basic dictionary form of the verb, meaning to buy.

After þarf að, Icelandic uses the infinitive:

• Ég þarf að kaupa
• Þú þarft að kaupa
• Við þurfum að kaupa

Only þurfa changes to match the subject; the main verb stays in the infinitive.

So:

• þarf = present tense, need
• kaupa = infinitive, to buy

Þarf is the present tense form of the verb þurfa for ég.

The verb þurfa means to need. Its present tense forms include:

• ég þarf = I need
• þú þarft = you need
• hann/hún/það þarf = he/she/it needs
• við þurfum = we need
• þið þurfið = you all need
• þeir/þær/þau þurfa = they need

So Ég þarf is simply the correct form for I need.

Because the preposition í takes the dative when it describes location.

Here, í búðinni means in the store, describing where the buying happens, not movement into the store.

Compare:

• í búðinni = in the store / at the store → location, so dative
• í búðina = into the store → movement toward/into, so accusative

Also:

• búð = store, shop
• búðin = the store (nominative)
• búðinni = the store (dative)

So í búðinni is exactly what you expect after í when the meaning is static location.

For the same reason as í búðinni: á takes the dative when it means location.

Here á horninu means on the corner or more naturally in English at the corner. It describes where the store is located.

Compare:

• á horninu = at/on the corner → location, dative
• á hornið = onto the corner / to the corner in certain movement contexts → accusative

So in this sentence:

• búðinni is dative after í
• horninu is dative after á

Both are location forms.

They mean different kinds of location:

• í búðinni = in the store
• á horninu = on/at the corner

So the full phrase is:

• í búðinni á horninu
• literally: in the store on the corner
• naturally: at the store on the corner / in the shop on the corner

This is a very common Icelandic pattern: one place phrase can contain another.

The main location is:

• í búðinni = in the store

Then that store is further identified as:

• á horninu = on the corner

Because Icelandic usually does not have a separate word like English the in front of nouns. Instead, the definite article is attached to the end of the noun.

Here:

• sjampó = shampoo
• no article is used, so it means shampoo in a general or indefinite sense

Compare:

• sjampó = shampoo
• sjampóið = the shampoo

So:

• Ég þarf að kaupa sjampó. = I need to buy shampoo.
• Ég þarf að kaupa sjampóið. = I need to buy the shampoo.

It is a loanword, but yes, it functions as an Icelandic noun.

In everyday use, sjampó usually means shampoo and is often treated as a neuter noun. In many contexts, the singular indefinite form stays the same:

• sjampó = shampoo

You may also see definite forms such as:

• sjampóið = the shampoo

For a learner, the important thing in this sentence is simply:

• kaupa sjampó = buy shampoo

You do not need to worry too much at first if some loanwords feel less regular than older Icelandic nouns.

This is just a normal prepositional difference between the languages.

Icelandic uses:

• á horninu

English usually says:

• on the corner or sometimes
• at the corner

So although á often means on, you should not translate it mechanically every time. In location expressions, it often matches natural English in less direct ways.

The best approach is to learn the whole phrase:

• á horninu = on the corner / at the corner

The basic order is:

• Ég = subject
• þarf = finite verb
• að kaupa = infinitive phrase
• sjampó = object
• í búðinni á horninu = place phrase

So the structure is:

Subject + verb + infinitive phrase + object + location

This is very normal Icelandic word order in a main clause.

Literal breakdown:

• Ég = I
• þarf = need
• að kaupa = to buy
• sjampó = shampoo
• í búðinni á horninu = in the store on the corner

Yes, but the tone is a little different.

• búð is very common and everyday: shop/store
• verslun can also mean shop/store, but it can sound a bit more formal or business-like depending on context

So:

• í búðinni á horninu sounds very natural in everyday speech

A learner should definitely know búð, because it is extremely common in ordinary Icelandic.

Then you would usually switch from location to movement, and that often changes the case after the preposition.

In this sentence:

• í búðinni = in the store → location → dative

If you mean into the store:

• í búðina = into the store → movement → accusative

For example:

• Ég fer í búðina. = I am going to the store / into the store.

This is one of the most important case patterns in Icelandic:

• í + dative for being somewhere
• í + accusative for going into somewhere

The same location-vs-movement idea also applies to many uses of á.