Við bætum moldina með því að setja moltu í hana.

Bætum is the 1st person plural present form of að bæta.

So:

• ég bæti = I improve / add
• þú bætir = you improve / add
• við bætum = we improve / add

Because the subject is við = we, the verb has to be bætum.

The ending -ina shows that the noun is definite: moldina = the soil.

In Icelandic, the is usually attached to the end of the noun instead of being a separate word as in English.

So:

• mold = soil
• moldin / moldina = the soil

In this sentence, the form is moldina because the noun is also in the accusative case.

Because moldina is the direct object of bætum.

The verb að bæta in this meaning takes an accusative object: you improve something.

So:

• Við bætum moldina = We improve the soil

By contrast, moldinni is a dative form, and that would not fit here as the direct object of bæta in this sentence.

Með því að is a very common Icelandic expression meaning by doing or by means of doing.

So:

• með því að setja moltu í hana = by putting compost into it

It is one of the standard ways Icelandic expresses the idea that English often gives with by + -ing.

On its own, því is the dative singular neuter form of það.

But in this sentence, you should mostly treat með því að as a fixed expression. It does not usually help much to translate each word separately in normal learning. The whole phrase simply functions like by doing.

A rough literal breakdown is something like:

• með = with / by
• því = that
• að setja = to put

But the natural meaning is just by putting.

Because að is the normal infinitive marker in Icelandic, like to in English.

So:

• setja = put
• að setja = to put

After með því að, Icelandic normally uses an infinitive:

• með því að setja = by putting

Even though English uses an -ing form, Icelandic uses að + infinitive here.

Because molta changes form here.

The noun is molta = compost, but after setja, it appears as the object, so you get the appropriate case form moltu.

So in this sentence:

• setja moltu = put compost

This is one of those noun forms that learners simply need to get used to seeing.

Because mold is a feminine noun in Icelandic.

Icelandic pronouns follow grammatical gender, not natural gender. So even though soil is an inanimate thing, it is referred to with the feminine pronoun form:

• hana = her / it (feminine accusative)

So í hana literally looks like into her, but in natural English it means into it, referring back to moldina.

Because í changes case depending on whether there is motion or location.

• accusative after í = motion into
• dative after í = location in

Here there is movement: compost is being put into the soil.

So:

• setja moltu í hana = put compost into it

If you were talking about compost already being inside the soil, you would use the dative:

• Moltan er í henni = The compost is in it

That motion/location distinction is very important in Icelandic.

They are different words, even though they look similar.

• mold = soil, earth, dirt
• molta = compost

So the sentence is talking about improving the soil by putting compost into it.

This pair can easily confuse English speakers because the forms resemble each other so much.

Yes. Við bætum moldina með því að setja moltu í moldina is grammatical.

But Icelandic, like English, often prefers a pronoun when the noun has just been mentioned. So í hana sounds more natural and less repetitive.

That is why the sentence uses:

• moldina first
• then hana to refer back to it

The sentence has very normal Icelandic word order.

• Við bætum moldina = main clause
• með því að setja moltu í hana = phrase explaining how it is done

So the structure is basically:

We improve the soil + by putting compost into it

You could move the með því að... phrase for emphasis in some contexts, but the given order is the most straightforward and natural.