Only the non-moveable feasts of the Church have a forefeast. The forefeasts helps to prepare the faithful for the feast itself. Special troparia and kontakia are assigned to the forefeasts, along the theme of the feastday.
Today, September 21, is the Leavetaking of the Exaltation of the Holy Cross. The feast was celebrated on September 14; the afterfeast (during which the theme of the feast day is continued) was seven days long.
On the eve of the feast, Vespers was celebrated, and afterwards, the cross, beautifully decorated, was brought out of the Altar while the choir and faithful sing "Holy God" from the Funeral Service.
After the Priest places the decorated cross on the center 'tetrapod' (a fancy term for a four-legged table with icons on it), the choir and faithful sing "Before Thy Cross" three times. Each time, the Priest circles the tetrapod, and censes the Cross at four points: facing east first, then facing north, then facing west, then facing south, finishing (and starting again) facing east.
For the Leavetaking (yes, I got back to it!), the process is reversed (mostly), and the Cross is taken back into the Altar. It seems to me not many parishes do this, but I could be wrong.
At the end of Liturgy, the priest comes out from the altar with a censer, preceded by a deacon with a candle. Going to the center of the church, he censes three times around the Cross. He takes the tray with the Cross and places it on his head to carry it into the altar. The deacon goes before him, censing the Cross. After placing the Cross on the altar, the priest censes the four sides of the Holy Table.
The Leavetaking also has the same Tropar and Kondak, the festal Prokiemenon, and the Hymn to the Theotokos.
Troparion — Tone 1O Lord, save Your people, /
And bless You inheritance. /
Grant victories to the Orthodox Christians /
Over their adversaries. /
And by virtue of Your Cross, /
Preserve Your habitation.
See this post of an Orthodox Church in Mays Landing, NJ, for a list of feast days and the length of the afterfeast and leavetaking.
Of course, for Pascha, the Feast of Feasts, the afterfeast and leavetaking is different: afterfeast is for 39 days, and the 40th day is the feast of Ascension. See more about this at the OCA website.