The cabeceo is the way people invite each other to dance. To ask someone to dance, a person will catch the eye of the person they want to dance with and nod their head. If the other person accepts the invitation they will nod back. If person does not want to dance for any reason, they will subtly look away, or not look toward that person to begin with.
The cabeceo ensures that no one dances out of obligation, and avoids rejection and hurt feelings. In traditional milongas of Buenos Aires, directly asking someone to dance is considered rude and is usually rejected.
In venues where cabeceo is difficult, the man may stand to get a better view, or walk around the room to get closer to the women he wants to ask to dance. But he still does the cabeceo from a distance and makes sure she has a mutual interest in dancing with him. If she accepts his invitation, he walks over to meet her. He does not cut across the floor or disturb other dancers who are already on the floor; he treats the dance floor as a sacred space. The woman should stay seated and maintain eye contact with the man until he meets her. This will avoid embarrassing situations where the cabeceo was intended for someone sitting next to the woman.
At the end of the tanda, the leader will accompany his partner back to her seat or wherever she requests to be taken.
The cabeceo happens at the beginning of the tanda, not during a cortina. This way, everyone is aware of what kind of music they may be committing to. Not looking around the room for the cabeceo at the beginning of a tanda will result in missed invitations to dance. Followers should use in the same seat all night so they can be easily located by leaders.
In traditional milongas, men and women wanting to dance with different partners are seated across from each other to make cabeceo easier to do. Couples who only dance with each other sit at their own table together, and other dancers will usually not invite them to dance.
It is polite to dance a full tanda with one person. However, if you start dancing partway through the tanda you still end at the cortina. A milonguero might ask a woman that he is unsure of to dance partway through a tanda so he can decide if he likes dancing with her without having to commit to an entire tanda.