Eftir rigninguna er auðveldara að draga illgresið upp úr moldinni.

Because eftir means after here in a time sense, and in that use it takes the accusative case.

• dictionary form: rigning = rain / rainfall
• accusative singular definite: rigninguna = the rain

So eftir rigninguna means after the rain.

In Icelandic, the is usually not a separate word. It is attached to the noun as an ending, and that ending changes with gender, number, and case.

Here you have:

• rigninguna = the rain
• illgresið = the weed / the weeds
• moldinni = the soil

So the different endings are not random; they show different grammatical forms.

Auðveldara is the comparative form meaning easier.

In Icelandic, when you say something like it is easier to..., the adjective is often put in the neuter singular form. That is why you get:

• er auðveldara að... = is easier to...

Auðveldari would be used when the adjective is agreeing with a masculine or feminine noun, not in this impersonal it is easier type of construction.

English needs a dummy subject: it is easier.

Icelandic often does not have to say that dummy subject explicitly in this kind of sentence, especially when something else comes first. So:

• Eftir rigninguna er auðveldara... = literally something like After the rain is easier...
• natural English: After the rain, it is easier...

You can also hear Það er auðveldara að..., but leaving out það here is completely natural.

Because Icelandic main clauses usually follow the verb-second rule.

That means the finite verb tends to come in the second position of the clause. Here:

1. Eftir rigninguna = first element
2. er = second element

So even though English and Icelandic do not always line up word-for-word, this word order is very normal in Icelandic.

Draga means to pull or to drag.

After auðveldara, Icelandic uses an infinitive with að:

• auðveldara að draga = easier to pull

So að draga illgresið upp means to pull the weeds up.

Because illgresi is often used as a collective noun in Icelandic. It can refer to weeds in general, even though the form is singular.

So:

• illgresi can mean weed growth / weeds
• illgresið can naturally correspond to English the weeds

This is one of those places where Icelandic and English package the idea a little differently.

It is the object of draga, so it is in the accusative case.

But illgresi is a neuter noun, and for many neuter nouns the nominative and accusative singular look exactly the same. So:

• nominative definite: illgresið
• accusative definite: illgresið

The case is different grammatically, even though the form does not change.

No. This is a false friend.

In Icelandic, mold means:

• soil
• earth
• dirt

It does not mean the fungus called mold in English.

So úr moldinni means out of the soil.

Because úr means out of / from, and úr takes the dative case.

That is why the noun appears as moldinni, which is the dative singular definite form of mold.

So:

• úr moldinni = out of the soil

Upp adds the idea of up.

So:

• draga = pull
• draga upp = pull up
• draga ... upp úr moldinni = pull ... up out of the soil

In other words, upp helps show that the weed is being pulled upward and out.

Yes, eftir rigningu could also work, but it means something slightly more general.

• eftir rigninguna = after the rain
  refers to a particular rain, or the rain that has just happened
• eftir rigningu = after rain / after a rainfall
  sounds more general

So the sentence with rigninguna feels more like a specific situation.