In the M.M. (Monster Manual) it says that PC (Player Characters) can become vampires.
It not good at all with mythology so I'm asking for a little help here.
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Much farther on in Vampire entry (p 297) in the stat block, there is an entry for the vampire's bite attack:
Bite (Bat or Vampire Form Only): Melee Weapon Attack: +9 to hit, reach 5 ft., one willing creature, or a creature that is Grappled by the vampire, Incapacitated, or Restrained. Hit: 7 (1d6 + 4) piercing damage plus 10 (3d6) necrotic damage. The target's hit point maximum is reduced by an amount equal to the necrotic damage taken, and the vampire regains Hit Points equal to that amount. The reduction lasts until the target finishes a Long Rest. The target dies if this effect reduces its hit point maximum to 0. A Humanoid slain in this way and then buried in the ground rises the following night as a Vampire Spawn under the vampire's control.
The italicized emphasis is mine, and details the canonical, in-game mechanism for converting humanoids (including PCs) into vampire spawn.
The step from vampire spawn to vampire is detailed earlier, on page 295:
If a true vampire allows a spawn to draw blood from its own body, the spawn transforms into a true vampire no longer under its master's control. Few vampires are willing to relinquish the control in this manner. Vampire spawn become free-willed when their creator dies.
[Interestingly, the rules-as-written imply that a vampire spawn whose creator vampire dies merely become free-willed vampire spawn, and do not get "promoted" to full vampire.]
[Equally interesting, a strict reading implies that True Vampire A can emancipate and promote the spawn of True Vampire B....]
Nothing precludes a GM from designing a setting with different or additional methods, of course.