Eftir jafnteflið útdeilum við spilunum réttsælis og skoðum bakhliðina.

That phrase sets the time frame for the whole sentence: after the draw/tie.

• eftir = after
• jafnteflið = the draw / the tie

So the sentence first tells you when the action happens, and then it gives the actions themselves.

The ending -ið is the definite article attached to the noun.

In Icelandic, the is usually added to the end of the word instead of appearing as a separate word.

• jafntefli = a draw / a tie
• jafnteflið = the draw / the tie

So this is not a random ending; it is the Icelandic way of saying the.

Útdeilum is the 1st person plural present form of the verb útdeila.

That means it corresponds to we deal out / we distribute.

You can break it down like this:

• út- = out
• deila = divide, distribute, deal

So útdeila means something like deal out or hand out/distribute.

This is because Icelandic is a verb-second (V2) language.

When a sentence begins with something other than the subject, such as a time phrase like Eftir jafnteflið, the finite verb usually comes next, and the subject comes after that.

So the order is:

• Eftir jafnteflið = first element
• útdeilum = verb in second position
• við = subject

A more English-like order would be Við útdeilum..., but after an opening phrase like Eftir jafnteflið, Icelandic normally prefers Eftir jafnteflið útdeilum við...

Because útdeila takes a dative object, and spilunum is the dative plural definite form of spil.

• spil = cards / playing cards (depending on context)
• spilin = the cards in nominative/accusative plural
• spilunum = the cards in dative plural

So the form changes because the verb útdeila requires that case.

It can mean different things depending on context, but here it clearly means cards.

That is because útdeila spilunum means deal out the cards, which fits card-game language very naturally.

So even if spil can have broader meanings in other contexts, here the verb makes the meaning clear.

Réttsælis means clockwise.

It is an adverb, so it describes how the cards are dealt out.

In this sentence:

• útdeilum við spilunum réttsælis = we deal out the cards clockwise

As an adverb, réttsælis does not change form here to agree with a noun.

Because the subject is still the same: we.

In coordinated sentences, Icelandic often leaves out the subject in the second clause if it is already clear.

So:

• útdeilum við ... og skoðum ...

means:

• we deal out ... and (we) look at ...

English does this too:

• We deal the cards and look at the back not necessarily
• We deal the cards and we look at the back

Bakhliðina is the definite accusative singular form of bakhlið.

• bakhlið = back side
• bakhliðina = the back side

The verb skoða normally takes an accusative object, so the noun appears in that form here.

So:

• skoðum bakhliðina = we look at the back side

Because Icelandic often uses the present tense when describing a procedure, a rule, or the next step in instructions.

So in a game-rule style sentence, the present tense can mean something like:

• then we deal out the cards
• we now deal out the cards
• the players deal out the cards

This is very normal in Icelandic. It is not necessarily talking about a literal ongoing action right this second; it can simply describe the standard step in the process.