Akatsuki hopefuls will need to find a current Akatsuki member and convince them to allow them to join the group. Generally only skilled ninja are accepted into the ranks of the Akatsuki.
The Akatsuki first emerged as a powerful group of S-ranked missing-nin that functioned as mercenaries for hire. Their real goals became clearer over time as they targeted the villages' jinchurikis to obtain the tailed beasts in accordance with a plan to initiate the Infinite Tsukuyomi on the moon to bring eternal and lasting peace. Since the time of the 4th Shinobi War, the organization died out.
Many decades after the 4th Shinobi War, the Akatsuki was resurrected by Kantaro Uzumaki, who stumbled across items of his uncle Nagato's during his travels as a missing-nin. He devised a plan and recruited a following to assist him with this goal. Initially this involved forming an alliance with Konoha. Whatever his plans were, they didn't get very far before he seemingly quit, turning the Akatsuki over to Masaki.
Since then the leadership and goals of the organization have changed several times. At one point a group known as the 'Masks' were the Akatsuki, though leadership and group composition has perhaps changed hands a few times since they were a group of influence. A man named Itamu has recently emerged, claiming he killed the previous Akatsuki and has taken over. He also claims that his goal are for peace.
The group is secretive and the exact membership and composition of the group, as well as it's goals, are unknown.