5th dnd – How do the bards prepare the spells?

Bards do not prepare spells in the 5th edition of D & D.

the Players Manual, Chapter 10: "Spellcasting", mentions that bards learn spells and can cast them spontaneously. The section "Known and prepared spells" says the following:

Before a caster can use a spell, he must keep it firmly in mind or have access to the spell contained in a magic object. Members of some classes, including bards and wizards, have a limited list of spells that they always know in the mind.

Instead of preparing spells, Bards simply have known spells, and they can use spell locations to cast one of their known spells. When creating a first-level bard, look in the PHB's spell-casting function, under the subsection "Known top-level spells and more":

You know four first-level spells of your choice in the list of bard spells.

The Spells column known from the bard table indicates when you will learn more about the bard spells of your choice. Each of these spells must be at a level for which you have spell locations, as shown on the chart. For example, when you reach the 3rd level of this class, you can learn a new 1st or 2nd level spell.

In addition, Bards learn a new spell (and can swap an old spell) each time they gain another level in the Bard class. You can read the full text of their Spellcasting feature on D & DBeyond.