You see it in movies many times, two enemy armies find each other but wait on the field, get ready, and fight later, maybe even the day after. Sure sometimes a messenger is sent, or the commanders meet to possibly avoid fighting or for some last insults before killing each other, but did they really wait for one another to be ready and eventually start the battle? Why not just attack as soon as your army is ready, having a tactical advantage over the unorganized enemy? Side question: is it also true that the soldiers would attack each other one by one? Like if I see two people fighting, I just have to find someone who is available and start fighting them? Movies raise a lot of questions :)
Ancient peoples certainly recognised the advantage of catching the enemy off guard, and actively tried to create situations in which they could attack before the enemy was ready. I've written about this in an older thread in response to a related question.
What you see in movies is a stylised version of something that might happen when such attempts failed. Once the armies were aware of each other's presence, they could encamp on opposite sides of a suitable battlefield and see what happened next. This stage could indeed involve both sides carefully deploying for battle, sometimes day after day, without a blow being struck. There might even be some last-minute negotiations (though movies tend to overplay this trope for narrative reasons: battle scenes are a big set-piece and these negotiations between key characters allow the writers to present the stakes as clearly as possible in the build-up to the climactic clash).
The reason for the delay is that pitched battle was generally understood to be a highly volatile business with immense risk to the troops on your own side. Generally only those who enjoyed overwhelming superiority were keen to fight a battle. Deploying against each other was both a game of chicken - giving the enemy a last chance to back away and yield - and an opportunity to gather intelligence about the enemy's troops and battle plans in an attempt to gain some advantage. It could also be a way to prepare your own troops for the coming battle; being drawn up in full array is an exercise that requires discipline and precision, and therefore acts as a form of training. It also inspires confidence to see your own army well-organised and prepared for battle.
If this prudent exercise gave the enemy time to prepare as well, that was an unfortunate side effect, not an intentional part of the ritual of pitched battle. If one side had fallen into ranks while the other was still forming up, the side that was ready would often take advantage of this. At the first battle of Mantineia (418 BC), the Spartans were taken by surprise when their Argive enemies appeared in the plain much earlier than expected; only their superior unit organisation saved the Spartans from being caught in disorder and overrun. At the second battle of Mantineia (362 BC), the Spartans were formed up and ready, but they were again surprised because their Theban enemies pretended to set up camp for the night, fooling the Spartans into thinking there would be no battle that day, then suddenly deployed for battle and advanced. There are many similar examples from Greek history; very few battles happened without one side or the other trying to engineer a last-minute advantage over the other.
Side question: is it also true that the soldiers would attack each other one by one?
I think you might be referring to the chaotic melee that movies like to turn premodern battles into. This is not what actually happened, at least not initially, while the formations were intact. I wrote about this in more detail here.