Ending an attunement and attuning to another object in the quickest way.

Let's say a character owns 4 magic items (A, B, C, and D) and is attuned to 3 of them, A, B and C.

They need to end the attunement to object C so to attune to D, use D to cast a spell (let's say Find Familiar) and then re-attune to object C. What is the quickest and most efficient way to do it RAW in terms of short rests and long rests?

Can they do it all during a single long rest?

Does it take 3 short rests? 

I was thinking, during the same short or long rest, another player could attune to object C thus ending the player attunement with it, but can it be done while the player is attuning with object D?

It takes one full Short Rest to attune to an item. It another full Short Rest to unattune to it.

• It would take three Short Rests to switch attunement back and forth.
• I believe a Long Rest can only take the place of one Short Rest.
• I character cannot start attuning to a new item unless they have an attunement slot available.

The first and third bullet points are described in the Attunement section.

• "Attuning to an item requires you to spend a Short Rest focused on only that item while being in physical contact with it (this can’t be the same Short Rest used to learn the item’s properties). This focus can take the form of weapon practice (for a Weapon), meditation (for a Wand), or some other appropriate activity. If the Short Rest is interrupted, the Attunement attempt fails. Otherwise, at the end of the Short Rest, you’re attuned to the magic item and can access its full magical capabilities."
• "You can be attuned to no more than three magic items at a time. Any attempt to attune to a fourth item fails; you must end your Attunement to an item first."

Your could increase the number of attunements.

They must go through the following steps

1. Unattune C
2. Attune D
3. Use D
4. Unattune D
5. Attune C

If they are by themselves, this will take 4 short rests. If they have a buddy available and that buddy has an empty attunement slot, this could possibly be accelerated (rules are not clear if you have have an empty attunement slot when you start attuning, or only when you finish).

An interesting thing I just noticed: a PC who dies and is revivified has all their attunements wiped.

The quickest is 4 Short Rest or 5 if Magic Item D need to be identified first.