Delay action clarification

When you delay, you are basically pausing your position in the initiative order. Recently I re-read the PHB and it had the following

"Coming Back into the Initiative Order: After any other combatant has completed a turn, you can step back into the initiative order. Perform your actions as desired and adjust your initiative to your new position in the order."

So, does that mean, for instance, if a character was first in the initiative and they elected to delay to the last to act in a round, that they are now last in the initiative for the rest of the encounter (or until someone else delays to a position after them)?

It makes sense (stops super-nova double actions, or someone delaying to make beneficial bonus's artifically apply longer), but admitadly, we havent been playing that way

Yes. When you Delay, you move down the initiative order until you act. Once you've acted, that's your new initiative for the rest of the encounter, unless you Delay again, or Ready.

While it's a matter of semantics, you can Delay 'past the bottom of the round' to go 'before' a higher initiative character. Initiative is cyclic, so that doesn't really mean anything, but you can do it.

And I want to make this note everywhere I can.

When you delay your turn your new initiative is (technically) lower than the person you finish your turn on.

For example.

You
Monster
Friend
Monster

If you want to delay your turn until your friend does something. That means your new initiative is

Monster
Friend
You
Monster

You can never share initiative with someone.