The Egyptian calendar was 365 days long, so it fell out of step with the seasons over time.
Egypt had three seasons:
Akhet - inundation/flood - the actual flood begins in mid-July and runs into October. During Ramesses III, New year's day (I Akhet I) fell in early May by the modern Gregorian calendar, about 9 weeks before the actual start of the flood and ran until sometime in September
Peret - season of emergence (planting and cultivation) - during Rameses III nominally runs from around Sep 10 - Jan 15
Shemu - harvest - approx Jan-May
Each season is divided into four months. Each month has a name, but was also referred to by number then season, e.g. IV Peret is the fourth month of Peret.
Each month is 30 days long and is divided into 3 tendays. The last two days of each tenday are days of rest for royal workers.
In addition to the seasons and months of the regular calendar, the five days prior to each new year are special and are celebrated as:
birthday of Osiris
birthday of Horus
birthday of Seth
birthday of Isis
birthday of Nephthys
Added to the 360 days of the regular seasons, these extra days make a 365 day year.
Wikipedia has a List of Festivals
Another article on some of the major festivals
The Opet festival (better pdf reference) is the major festival in Waset (the ancient Egyptian name for Thebes/Luxor). It is a fertility ritual in which the god Amun from Karnak temple goes for a conjugal visit with the goddess Mut in her temple at Luxor. They also parade ceremonially through the settlements on both sides of the Nile, along with their son Khonsu. The Opet festival was celebrated during the actual inundation, so in year 8 of Rameses III it will commence on III Akhet 5 and run for 24 days. During each Opet, Pharaoh marries his father Amun in a ritual to revitalize his own divinity and ensure Egypt's fertility for the coming season of Peret. (OK, found a historical reference placing Opet : "the Opet Feast, which was celebrated from II Akhet 19 to III Akhet 15 in the time of Ramses III " The Opet Feast was intended to take place near the peak of inundation.
I'm not sure of the actual chronology, but Opet may have been tied to the new moon. According to Sky Safari, there would have been a new moon on July 13th and August 11th, 1178. We'll take the start of Opet to be August 11th, as medieval records place the typical peak of the Nile inundation during late August or September, sometimes as late as October.
In the campaign world, the Festival proceeds as follows:
on the morning of the first day, the statues of Amon, Mut and Khonsu are washed, dressed and placed in their royal barques. The barques are carried along the processional way.
the processional way is lined with ram-headed sphinxes. As the Amon's barque draws even with a sphinx, it animates and bows to the god. When Mut's (the last) barque passes, the sphinx returns to its orignal pose and reverts to stone.
There are six stations along the processional way where rituals are performed. All the people of Waset may witness and attend these rituals. In practice, it's only possible for any individual to get close to one or maybe two of them: crowding prevents free access except for very high ranking individuals. The choice of ceremony to attend depends on profession, class, gender and personal circumstance.
The 2km procession takes from first light to sunset. A sunset ritual is performed in the Luxor temple courtyard, after which the statues of Amon and Mut are placed in the birthing chamber to recharge. The festival ends when the gods are fully charged.
Pharaoh is ritually married to Amon in the evening ceremony at Lusor temple. The remainder of Opet can be seen as the marriage feast.
The marriage of Amon to Mut is then ceremonially consummated, with Pharoah and his Great Wife standing in for the gods. The royal/divine couple then retires to a chamber in the temple to have sex for a few days to renew the fertility of the Black Land (Kemet).
Once the gods have fully recharged, Pharaoh enters the birthing chamber to refresh his own divine energy. In Hatshepsut's time, the gods charged in 11 days. That has been getting slower over time. This year, it's expected to take 24 days.
After Pharoah emerges recharged from the birthing chamber, the gods are placed back in their barques and carried back to Karnak temple, stopping again at each station along the way.
For each procession, statues of the triad are also loaded onto a barge which is towed along the Nile in the same direction. This is a security measure to ensure that at least one copy of each god makes it to the birthing chamber in Luxor temple (ipet resyt , the southern sanctuary), Those without a pressing need to attend the ceremony at one of the stations line the banks of the Nile to cheer the passage of the gods on the barge.
More notes: "The whole route was lined with cheering multitudes as the god proceeded down the sphinx lined avenue. The wab-priests (‘purifiers’), with their shaven heads and bleached white linen robes, shouldered the burden of the three barques (left). They were accompanied by other priests wearing leopard skin mantles along with large numbers of fan-bearers, musicians, singers and acrobatic dancers. The spectacle would have been magnificent as the procession passed by, and the crowds delirious with joy. Along the way, Hatshepsut established six way stations where the priests could put down their burden and let a new group take it up. The last of these was just outside the entrance to the temple but was entirely rebuilt by Ramesses II and enclosed "
"Something of the power of the god was transferred to the royal ka, topping up the royal batteries so to speak. In return, the pharaoh, through offerings and the performance of such rituals as the Opening of the Mouth, set in motion a new cycle of creation and re-ignited the sacred spark within the god. The Sacred Marriage between Amun and Mut was re-consummated—with the pharaoh and his queen acting as stand-ins—and the divine pair took a few days honeymoon in the seclusion of the temple. This proper performance of this fertility ritual was absolutely vital to the continued good order of the universe and there was a strong erotic element to the proceedings. "