When do we read the Song of Songs?

There are a number of customs; here are a few:

Many have the custom to read the Song of Songs on the Shabbat of the intermediate days of Passover before the morning Torah reading. If there is no Shabbat during the "intermediate days," then the Song of Songs is read on the morning of the Seventh Day of Passover.

The Song of Songs talks of the love between husband and wife -- an analogy for the passionate love between G‑d, the supernal groom, and His beloved bride Israel. This "romance" began to bloom and flower when He descended to take His bride out of Egypt on Passover.

Following the same reasoning, many read the Song of Songs after the Passover Seder.

There a custom among many Sephardim to chant the Song of Songs every Friday night before the evening service. Many chassidim read the Song of Songs every Friday afternoon, in preparation for the holy Shabbat.

I hope that I've been helpful today.

Yours truly,

Rabbi Menachem Posner