How can a muggle become a wizard?

They can't. Muggles have no magical blood and therefore cannot do magic. However, squibs can sometimes learn magic from special courses so perhaps this would work with muggles. Although ,no indication has ever been made that muggles can become magical other than through birth i.e. just being born magical. However, there is the situation albeit rare where magical abilities may for some reason stay dormant through adulthood. When these abilities surface it may seem to everyone involved that the impossible happened, a muggle became a witch/wizard!