There are 2 definitions of "round" in 5e. There is the definition of "round" that you quote, which is from initiative position intMax to initiative position 0 (or negative if you manage that some how).
Then there is the definition used here for readied actions. This is the same definition used in "once per round" effects such as certain powers. This definition begins at the beginning of your turn and ends at the beginning of your next turn.
Because (unlike in 4e), readying an action and activating it, doesn't move your initiative order position, and because it matches the readied action refresh timer (which happens to use the same 1/round definition of round), readied actions can be used at any point in either the current round or the next round prior to your turn.
Here's how reactions refresh:
When you take a reaction, you can’t take another one until the start of your next turn. If the reaction interrupts another creature’s turn, that creature can continue its turn right after the reaction. (Player's Basic p70)
This is a large part of the support that leads me (and many others) to believe that readied actions can roll up to your next turn.
Your Turn
On your turn, you can move and perform an action. The ready action is, as you point out, an action like any other. This means that on your turn you can move and take the ready action.
The Ready Action
The ready action allows you to react to a specific, "perceivable circumstance."
To do so, you can take the Ready action on your turn so that you can act later in the round using your reaction.
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.
Remember that "[a] reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else's," (Reactions), meaning it happens immediately after the trigger occurs.
Your Questions
However can you move on the same turn that you ready an action?
Yes, you can. It is an action just like any other, and is taken on your turn.
Secondly when the trigger goes off do you have to wait for your turn or do you in effect get a bonus turn?
It's a reaction, and happens immediately. It's not another turn, nor do you have to wait. It happens when the trigger, well, triggers it. Reactions can—and almost always do—occur on someone else's turn.
Caveats
A few notes on the ready action.
- It takes up your reaction, so you can't perform the readied action and an opportunity attack in the same combat round
- The readied action happens when the trigger occurs, but any movement has to be done on your turn—unless your reaction is to move. It does not move your turn in the initiative order
- Spells used for a readied action gives that spell a concentration requirement, and thus doesn't work if you already are concentrating on a spell (or you could choose to stop concentrating on it)
Best Answer
This is the general case. Chapter 9 gives rules that tell what you need to do when a encounter requires the characters to resolve their actions within combat.
There is nothing that forbids a referee to apply any or all of the combat rules while the characters are exploring a dungeon or moving around. But there is nothing specific either so the referee has to fall back to the general rule of How to Play as described on Page 6.
The effect of readying a action is that the player forgoes his normal action in favor being able to use his reaction to do a specific action under specific conditions. If the conditions do not occur by the start of the player's next turn then it is effectively lost. This especially important in case of casting a spell.
Keeping a spell ready outside of combat is not practical as the caster will quickly lose all of his spells before an encounter. Readying a bow or another weapon is more practical. So lets look at that situation.
A typical character gets a movement and a action. This action can include a dash which increases the character effective movement rate. So the first effect is that character can't dash and keep his bow ready at the same time.
Now we have a party moving slowly and the character has his bow ready. Perhaps with a condition that I shoot anybody who attacks the party. Remember the person doing a ready action has the option of ignoring the trigger. The party enters into a combat encounter.
First off what if there is surprise? On page 189 it clearly states that during surprise no character or monster can take a move or action during the first turn of combat if there is surprise. Furthermore it says that those who are surprised can't take a reaction until that turn ends.
Since you determined the initiative order at the start of combat. This means the person with a ready action will lose if they are surprised. During the first turn the initiative will eventually pass to the surprised character who is unable to use his reaction until the end of the turn, and is unable to take any actions on his turn.So in my example the character with the ready bow is unable to fire.
If the character isn't surprised then having a Ready Bow (or weapon) could be a help as the character can take his reaction immediately at the beginning of the turn provided that the condition is met.
The rules doesn't address this specifically. But it does have an example of movement with stealth checks on page 182, specifically moving at a slow rate of speed. It would reasonable to rule that if a character is moving slowly they can have a ongoing Ready action. However I would also rule it is one or the other. Either you moving slowly and effectively taking the Hide action to make a stealth check, or your moving slowly and effectively making a Ready action to be on alert for something.
The Ready Action and readied spells
A readied spell require concentration with no time limit specified. All good except six seconds later when your turn comes you have to take an action. Your Ready action no longer applies and you have to take another Ready action. The way the rules read your character action status resets at the beginning of his turn.
What happens if you have a readied spell? The rules don't specify. Thus leaving it up to the referee to make a judgment call.
A case could be made for both which one prevails depends on the referee personal view of what happens to the spell energies when it is readied. Is there is a time limit? Or it can be held indefinitely as long as concentration is maintained.