Í uppskriftinni stendur að við þurfum tvær matskeiðar af olíu og hálfa teskeið af salti.

This is normal Icelandic word order. Icelandic is a verb-second language, so if you put something else first for context or emphasis, the finite verb still comes second.

So:

• Í uppskriftinni = first element
• stendur = second element, as required
• að við þurfum... = the rest

A very literal structure is: In the recipe stands that...

Because í here means in in a location sense, and that normally takes the dative case in Icelandic.

The noun is uppskrift = recipe
Its definite form is uppskriftin = the recipe
After í for location, it becomes dative: í uppskriftinni = in the recipe

So the -inni ending shows both:

• the
• dative singular

Stendur is the present tense of standa, which literally means stand. But in written contexts Icelandic often uses standa the way English uses say, be written, or state.

So Í uppskriftinni stendur að... means something like:

• It says in the recipe that...
• The recipe states that...

It is a very natural Icelandic way to talk about what is written in a text.

Here að means that and introduces a subordinate clause:

• stendur að við þurfum...
• it says that we need...

This is very common in Icelandic after verbs of saying, thinking, knowing, and similar ideas.

Við means we, and þurfum is the 1st person plural present form of þurfa = to need.

So:

• ég þarf = I need
• við þurfum = we need

In sentences like this, Icelandic often uses a general we where English might also say we, you, or just phrase it differently depending on style.

Because Icelandic numbers from one to four change form to match the gender of the noun, and often also the case.

Matskeið is a feminine noun, so two must be in the feminine form:

• masculine: tveir
• feminine: tvær
• neuter: tvö

So tvær matskeiðar is correct because matskeið is feminine.

Because the noun is plural here and it is the direct object of þurfum.

The basic singular noun is:

• matskeið = tablespoon

Here we need two tablespoons, so it becomes plural:

• tvær matskeiðar

This is the correct plural form for this feminine noun in this context.

Because hálfa has to agree with teskeið in gender, number, and case.

Teskeið is:

• feminine
• singular
• here used as the object of þurfum, so it appears in the accusative

That gives:

• hálfa teskeið = half a teaspoon

Also, the noun stays singular because it means half of one teaspoon, not multiple teaspoons.

In Icelandic, quantities and measures are very often followed by af to mean of:

• tvær matskeiðar af olíu = two tablespoons of oil
• hálfa teskeið af salti = half a teaspoon of salt

So this is the normal way to express an amount of some substance.

Because af takes the dative case.

So:

• olía becomes olíu
• salt becomes salti

That is why you get:

• af olíu
• af salti

A useful detail: olíu happens to look the same in more than one case, but salti clearly shows the dative ending.

Yes.

• matskeið literally means something like food spoon
• teskeið literally means tea spoon

But in normal usage they simply mean:

• tablespoon
• teaspoon

So you should learn them as standard measurement words in recipes.

Yes, you could. Uppskriftin segir að... means the recipe says that... and is perfectly understandable.

But í uppskriftinni stendur að... is especially natural when talking about what is written in a text. It has a slightly more literal it stands in the recipe that... feel, which Icelandic uses very naturally.