Apollodorus relates to an unnamed companion a story he learned from Aristodemus about a symposium, or dinner-party, given in honor of the tragedian Agathon. Socrates arrives at the party late, as he was lost in thought on the neighboring porch. After they have finished eating, Eryximachus picks up on a suggestion of Phaedrus', that each person should in turn make a speech in praise of the god of Love.
Phaedrus begins by saying that Love is one of the oldest of the gods, and the one that does the most to promote virtue in people. Pausanias follows Phaedrus, drawing a distinction between Common Love, which involves simple and mindless desire, and Heavenly Love, which always takes place between a man and a boy. In the case of Heavenly Love, the boy, or loved one, sexually gratifies the man, or lover, in exchange for education in wisdom and virtue. After Pausanias, Eryximachus, the doctor, speaks, suggesting that good Love promotes moderation and orderliness. Love does not restrict itself to human interaction, but can be found in music, medicine, and much else besides.
The next to speak is the comic poet Aristophanes. Aristophanes draws an engaging myth that suggests that we were once all twice the people we are now, but that our threat to the gods prompted Zeus to cut us in half. Ever since, we have wandered the earth looking for our other half in order to rejoin with it and become whole. Agathon follows up Aristophanes, and gives a rhetorically elaborate speech that identifies Love as young, beautiful, sensitive, and wise. He also sees Love as responsible for implanting all the virtues in us. Socrates questions Agathon's speech, suggesting that Agathon has spoken about the object of Love, rather than Love itself.
In order to correct him, Socrates relates what he was once told by a wise woman named Diotima. According to Diotima, Love is not a god at all, but is rather a spirit that mediates between people and the objects of their desire. Love is neither wise nor beautiful, but is rather the desire for wisdom and beauty. Love expresses itself through pregnancy and reproduction, either through the bodily kind of sexual Love or through the sharing and reproduction of ideas. The greatest knowledge of all, she confides, is knowledge of the Form of Beauty, which we must strive to attain.
At the end of Socrates' speech, Alcibiades bursts in, falling-down drunk, and delivers a eulogy to Socrates himself. In spite of Alcibiades' best efforts, he has never managed to seduce Socrates as Socrates has no interest at all in physical pleasure.
Soon the party descends into chaos and drinking and Aristodemus falls asleep. He awakes the next morning to find Socrates still conversing. When everyone else has finally fallen asleep, Socrates gets up and goes about his daily business as always.
You do not have to look outside you as everything is in your "self", everybody is the two energies (woman-man/yin-yang/...) and if you awaken your "opposite" you are "one", you are realized, totally happy. This is called e.g. in the Bible the Holy or Mystic Marriage. Also the alchemists describe it as "Coniunctio Oppositorum", the Philosopher's Stone, make Gold from Lead,... See the writings of the Mystics too. Etc.