Ég kann að elda einfaldan kvöldmat.

In this sentence, að is the infinitive marker, similar to English to in to cook.

• kann = can / know how to
• að elda = to cook

So Ég kann að elda literally means I know how to cook.

This is a normal pattern with kunna when it means knowing how to do something. English often drops to after can, but Icelandic uses að here.

kann is from the verb kunna, and here it means to know how to or to be able to because of learned skill.

So:

• Ég kann að elda = I know how to cook / I can cook
• It suggests ability based on knowledge or skill.

By contrast, geta often means can / be able to in a more general sense, often about possibility or capability:

• Ég get eldað = I can cook
  This can simply mean I am able to do it.

A useful rough distinction is:

• kunna = know how, have learned
• geta = can, be able, be possible

In many everyday sentences, both may translate as can, but kunna is especially common for learned abilities.

Because að elda is the infinitive, the basic dictionary form of the verb to cook.

After kann, Icelandic uses the infinitive:

• Ég kann að synda = I can swim
• Ég kann að skrifa = I can write
• Ég kann að elda = I can cook

So elda is not conjugated here because kann is the conjugated verb, and að elda is the infinitive phrase that follows it.

Because einfaldan must agree with kvöldmat in gender, number, and case.

Here, kvöldmatur is:

• masculine
• singular
• in the accusative case as the direct object of elda

So the adjective also has to be masculine singular accusative:

• nominative: einfaldur
• accusative: einfaldan

That is why the sentence has:

• einfaldan kvöldmat

not:

• einfaldur kvöldmatur
• einfalt kvöldmat

The dictionary form is kvöldmatur (dinner / evening meal), but here it is in the accusative singular because it is the direct object of elda.

So:

• nominative: kvöldmatur
• accusative: kvöldmat

This kind of change is common in Icelandic masculine nouns.

So:

• Kvöldmaturinn er góður. = The dinner is good.
• Ég elda kvöldmat. = I cook dinner.

Icelandic often leaves the indefinite article untranslated because it does not have a separate word for a/an like English does.

So:

• einfaldan kvöldmat = a simple dinner

There is no separate Icelandic word for a here. The noun phrase is indefinite just by being used without the definite ending/article.

Compare:

• kvöldmat = dinner / a dinner
• kvöldmatinn = the dinner

It is in the accusative case because it is the direct object of the verb elda.

In this sentence:

• Ég = subject
• kann = finite verb
• að elda = infinitive phrase
• einfaldan kvöldmat = what is being cooked

Since kvöldmat is the thing being cooked, it takes the accusative.

The adjective einfaldan also goes into the accusative to match it.

The basic structure is:

• Ég = I
• kann = can / know how
• að elda = to cook
• einfaldan kvöldmat = a simple dinner

So literally:

• I know-how to cook a simple dinner

This is a very normal Icelandic sentence pattern: subject + finite verb + infinitive phrase + object

Because Icelandic is a V2 language in many contexts, the finite verb often comes early in the clause. In a simple statement like this, the subject comes first and the conjugated verb follows immediately.

Yes, that is also possible, but it is not exactly the same in nuance.

• Ég kann að elda einfaldan kvöldmat = I know how to cook a simple dinner
• Ég get eldað einfaldan kvöldmat = I can cook a simple dinner

The first focuses more on learned skill/know-how.
The second focuses more on ability/possibility.

In many everyday situations, both could be translated the same way in English, but kunna is especially good when talking about something you have learned to do.

A rough English-friendly guide would be:

• Ég ≈ yeg
• kann ≈ kan
• að ≈ ath or a very light ahth
• elda ≈ EL-ta
• einfaldan ≈ AYN-fal-dan
• kvöldmat ≈ kvuhtl-maht or kvœld-maht depending on how detailed you want to be

A few useful notes:

• ð is like the th in this, though it can be weaker in actual speech.
• ll in Icelandic often does not sound like English ll.
• kvöld can be tricky because of the consonant cluster.

If you want a simple stress rule: Icelandic words are usually stressed on the first syllable.

Yes. Literally, kvöldmatur is something like evening food/meal:

• kvöld = evening
• matur = food / meal

In actual usage, it usually means dinner or evening meal.

So einfaldan kvöldmat is a very natural way to say a simple dinner.

Yes, absolutely.

• Ég kann að elda. = I can cook / I know how to cook.

The phrase einfaldan kvöldmat just adds more information about what you can cook.

So the full sentence means something like:

• I know how to cook a simple dinner

But without the object, the sentence is still complete and natural.