Ég var heppinn í dag.

Because var is the past tense of vera (to be).

• ég er = I am
• ég var = I was

So in Ég var heppinn í dag, var shows that the sentence is talking about being lucky earlier today or at some point today, not necessarily right now.

Var is the 1st person singular past tense form used with ég (I), but it is also the same past-tense form for he/she/it.

Examples:

• ég var = I was
• hann var = he was
• hún var = she was
• það var = it was

So Icelandic does not always have a different past-tense form for every person.

Heppinn is an adjective, and Icelandic adjectives must agree with the noun or pronoun they describe.

Here it describes ég (I), so the form depends on the speaker’s gender:

• Ég var heppinn í dag. = said by a male
• Ég var heppin í dag. = said by a female

So heppinn is the masculine singular nominative form.

Only the adjective changes:

• Ég var heppin í dag.

That is because the adjective must match the speaker’s gender.
The rest stays the same:

• Ég = I
• var = was
• í dag = today

Because it is a predicate adjective after the verb vera (to be).

In Icelandic, when an adjective comes after vera and describes the subject, it is usually in the nominative, matching the subject.

So:

• Ég is the subject
• heppinn describes ég
• therefore heppinn is in the nominative singular masculine

This is similar to how in English we say I was lucky, where lucky describes I.

Í dag literally means in day, but idiomatically it means today.

This is a very common fixed expression in Icelandic.

Examples:

• í dag = today
• í gær = yesterday
• á morgun = tomorrow

Even though í often means in, you should learn í dag as a whole expression meaning today.

The noun dagur (day) appears here in the form dag, because the preposition í can govern different cases, and in this expression it takes the accusative.

So:

• dictionary form: dagur
• accusative singular: dag

That gives:

• í dag = today

This expression is so common that many learners memorize it as a set phrase.

Yes. Icelandic word order is flexible, especially with time expressions.

You can say:

• Ég var heppinn í dag.
• Í dag var ég heppinn.

Both are natural. The second version puts more emphasis on today.

Because Icelandic is a verb-second language, if you start the sentence with Í dag, the finite verb usually comes next:

• Í dag var ég heppinn.

Not: Í dag ég var heppinn.

A rough English-friendly guide is:

• Ég ≈ yegg (with a y sound at the start)
• var ≈ vahr
• heppinn ≈ hep-pin
• í ≈ ee
• dag ≈ dahg

A few pronunciation notes:

• é in Icelandic sounds like ye
• g at the end of Ég is pronounced, unlike in English I
• pp in heppinn is a clear double consonant
• á and a sounds are different in Icelandic, so listen carefully when learning related words

A more Icelandic-like approximation would be something like:

Yeg var hehp-pin ee dahk

but exact pronunciation is best learned from audio.

Yes, heppinn / heppin is a common everyday word for lucky.

A related noun is:

• heppni = luck

Examples:

• Ég hafði heppni með mér. = I had luck on my side.
• Þú ert heppinn. = You are lucky.
• Hún er heppin. = She is lucky.

For most ordinary situations, heppinn/heppin is the natural adjective to learn first.

Normally, learners should understand it as I was lucky today.

The sentence is neutral and straightforward in Icelandic.
If English speakers are thinking of the slang meaning of got lucky, that meaning is not what this sentence automatically suggests. Context matters, but by default it simply means that the speaker had good luck today.

Usually, no. Icelandic normally keeps the subject pronoun, unlike some languages where it can be dropped.

So you would normally say:

• Ég var heppinn í dag.

Leaving out ég would usually sound incomplete unless the context is very special, such as notes, poetry, or very informal fragments.

The structure is:

• Ég = subject
• var = verb
• heppinn = predicate adjective
• í dag = time expression

So the pattern is:

Subject + verb + adjective + time phrase

This is a very useful pattern in Icelandic. For example:

• Ég var þreyttur í morgun. = I was tired this morning.
• Hún var glöð í gær. = She was happy yesterday.

So this sentence is a good model for many similar sentences.