Þú getur fengið þér vatn.

A close word-for-word breakdown is:

• Þú = you
• getur = can
• fengið = get / receive, from the irregular verb fá
• þér = yourself / for yourself
• vatn = water

So the literal idea is You can get yourself water.

In more natural English, that often comes out as:

• You can have some water
• You can get yourself some water
• Help yourself to some water

Because Icelandic very often uses the pattern fá sér + noun for getting or having something for your own use, especially food and drink.

So:

• fá vatn = get water
• fá sér vatn = get oneself some water / have some water

In this sentence, þér adds that for yourself idea. In English, we often do not translate it very explicitly.

Þér is the dative singular form of þú.

That may feel strange at first, because English just uses you for everything. Icelandic changes pronouns by case.

Here, the pattern fá sér takes a dative pronoun:

• Ég fæ mér vatn = I get myself some water
• Þú færð þér vatn = You get yourself some water
• Hann fær sér vatn = He gets himself some water

So in your sentence, þér is there because that is the form this expression uses.

This is one of the things learners notice quickly: fá is a very irregular verb.

Some important forms are:

• fá = dictionary form
• fæ / fær = present tense forms
• fékk = past
• fengið = another common form you will see often

In the very common pattern geta fengið sér + noun, Icelandic uses fengið. The safest beginner strategy is to learn fá sér and geta fengið sér as common chunks.

The important thing to remember is that fá and fengið belong to the same verb.

Because getur is the correct present-tense form of geta for þú.

A short present-tense pattern is:

• ég get = I can
• þú getur = you can
• hann/hún/það getur = he/she/it can
• við getum = we can
• þið getið = you can
• þeir/þær/þau geta = they can

So even though English has you can, Icelandic uses the form getur here.

It depends a little on context, but in everyday use it often sounds like an offer or a mild permission:

• You can have some water
• You can help yourself to some water

Strictly speaking, geta often means can / be able to. If you want a clearer sense of may / are allowed to, Icelandic often uses mega instead:

• Þú mátt fá þér vatn = You may have some water / You are allowed to have some water

So your sentence is natural, but its exact shade in English depends on the situation.

Because Icelandic often leaves that unstated, especially with mass nouns like water.

So vatn can mean:

• water
• some water

depending on context.

English often requires or strongly prefers some in this kind of sentence, but Icelandic does not.

Because vatn means water in a general, indefinite sense.

• vatn = water / some water
• vatnið = the water

In this sentence, the meaning is not the water as a specific already-known thing. It is just water in general, so vatn is the natural choice.

It is the direct object, so it is in the accusative.

However, vatn is a neuter noun, and in the singular its nominative and accusative forms look the same. So you do not see any spelling change here.

That is very common in Icelandic neuter nouns.

Because short pronouns like þér usually come before the full noun object in this kind of expression.

So fá þér vatn is the normal, natural order.

You can think of it as:

• first the small pronoun
• then the thing being gotten

This is a very common Icelandic word-order pattern.

Yes, but the nuance changes a little.

• Þú getur fengið vatn = You can get water / You can receive water
• Þú getur fengið þér vatn = You can get yourself some water / You can have some water

With food and drink, fá sér is often the more natural idiomatic choice when someone is having something for themselves.

The letter þ is pronounced like the th in thin, not like the th in this.

So:

• þú sounds roughly like thoo
• þér sounds roughly like thyair or thyer, depending on accent

A useful rule:

• þ = unvoiced th, as in thin
• ð = voiced th, as in this

Your sentence only has þ, but learners often want to know that contrast early.