The first round is called Round 1. The round begins with the "Summoning Phase". During the Summoning Phase your deity is able to place any Creatures or Immortals in your deck. The only thing stopping you from placing a Creature/Immortal is if you do not have enough mana to summon it.
Here is a screenshot that shows the battlefield with with your rune brigade (deck). The rune brigade is currently stationed inside the castle. You can scroll through your list of runes inside the castle using the scroll arrows. You can view 3 runes to start the 1st round and then 2 more are turned over after that.
Note: This is placeholder art and later the "Castle" will look more like an actual castle. Notice also how your deity is currently highlighted (blue in this case) when you are currently in the summoning phase.
Once you have finished summoning any creatures you end your turn. In a multiplayer game you wait until the other player is finished and then play begins (you actually place summoned units simotaneously). And then both players see the battlefield with the newly summoned creatures and/or immortals.
After this initiative is calculated and the creature or immortal with the lowest initiative plays their turn.
Now is the time to go into primary and secondary turns. Remember, there are two rounds. There is the main round and the 1/2 round. In this example we are in the main round (Round 1). After all creatures/immortals have played their turn we will go on to the 1/2 round (Round 1.5).
I explain this because this character must now decide to use a primary or secondary attack in this first part of the round. A primary attack is a melee or ranged attack or a spell. A secondary attack is a potion, discipline, creature ability, or magic item.
The reasons to use a primary or secondary attack to start the round are many and vary depending on strategy and creature/immortal currently taking a turn. You might want to start off with your strongest attack (likely a spell or physical attack) to do the most damage right away. Or you may want to use a discipline/potion to boost your abilities so that in the 1/2 part of the round your strongest attack will actually be more powerful.
Anyway, more on that some other time with specific examples. The main thing here is that you can only use one primary attack per round. If you use your primary attack right away then the second part of the round (1/2 round) you must use a secondary attack. However, if you don't want to use a primary attack at all you can use two secondary attacks in a round if you wish (if you feel this will help you in the battle somehow).
Alright, so once all of the creatures and immortals have played their 1st turn we go back to the castle once again. But this time the runes are not played simotaneously. Instead, the player/deity with more mana plays first. This is because in this 1/2 round part of the round only spells/relics may be played. Not creatures or immortals.
So, the deity then plays all the spells or relics he wishes to play and ends his turn. Then he ends and the other deity plays. Here is a screenshot of this. The only difference between this castle and the other is the "C" instead of the "S" right now. But later the runes will be greyed out if they can't be played at the current time.
And once both deities have played the initiative begins again (from the beginning). After this round is over we begin again with round 2 and we continue from there.
After each round new mana is gained as well. Mana will be discussed in greater detail later.
In games, these "round halves" are usually called phases. Maybe an "attack phase" and a "support phase" ... or something :P