How does the Ready action work?

Question

So from reading the Player's Handbook, it seems that the Ready action is taken instead of any other action as it is an action in its own right. However, can you move on the same turn that you ready an action? For instance, (taking the example from the Player's Handbook):

If the cultist steps on the trapdoor, I’ll pull the lever that opens it

Presumably, when you ready this action, you would want to move near to the lever so you can pull it when the time is right. Likewise, with readying a spell, you would obviously want to move away from combat so you could concentrate on the spell.

Secondly, when the trigger goes off do you have to wait for your turn, or do you in effect get a bonus turn? For instance, the cultist starts running towards you, but on his way he steps on the trap door - so you immediately pull the lever, even though it wasn't your turn. I assume you then act as normal when your actual turn comes around?

Answer 1

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)

Answer 2

On your turn you have 4 types of actions, 3 limited (action, move action, bonus action) and 1 free (free action).
When you ready an action, you store your action for later use (using your reaction). You still perform your move, bonus, and free actions on your turn. This means you would be able to move to the lever that opens the trap door on your turn, then ready an action to pull the lever when the cultists steps on the trap door.

Once the trigger goes off, you interject in the narrative to complete your turn by using your reaction to perform your readied action. In this way, it is very similar to an attack of opportunity. Once your readied action is completed, control goes back to the way it was (the cultist's turn) and all continues as normal.

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From a player's perspective, their character has recognized a possible opportunity which will occur in the near future. Rather than continuing with the frenzy of battle, they chose to wait until that opportunity is available. The character is still alert, mobile, and defending themselves; but they have not done anything which might distract them from the pending opportunity. This way, they do not miss the opportunity in the frenzy of the battle.

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Update: To be clear, you can ready your move action instead of your action, but you cannot do both (thanks to J. A. Streich for pointing this out). Per Jeremy Crawford, lead rules designer for 5e:

When you use Ready, you prepare an action or a move, not both.