Julian Calendar

The Julian calendar (devised by Julius Caesar in 46 BC) is basically the same as our modern (Gregorian) calendar. It had 355 days and 12 months (roughly based on moon phases) with an extra day added to February every 4 years. Caesar updated an existing Roman calendar. Mensis intercalaris

Days of the Week
The days of the week were similar too:

Dies Lunae (Named after Luna, the Roman moon goddess)

Dies Martis (Named after Mars)

Dies Mercurii (Named after Mercury, the god of messengers)

Dies Iovis (Named after Jupiter, the king of the gods)

Dies Veneris (Named after Venus, the goddess of love)

Dies Saturni (Named after Saturn, the god of sowing or seed)

Dies Solis (Dies means "day." Named after Sol, the Roman sun god)

Months
The Julian calendar also had 12 months (most months had 29 days):

Ianuarius (29 days) (named after the god Janus, who has two faces and is the protector of gates and doorways)

Februarius (28 days) (Latin "februa" means "to cleanse." This month was named after Februlia, which took place during this period.)

Martius (31 days) (Named after the god of war: Mars. This was the time of year to resume military campaigns after the pause because of winter)

Aprilis (29 days) (Latin "aperio" means "to open (bud)." Since plants begin to grow in this month, it was viewed as spring's renewal)

Maius (31 days) (Named for the goddess Maia, who oversaw the growth of plants. Also, elders (Latin: maiores) were celebrated this month)

Iunius (29 days) (Named after goddess Juno, patroness of marriage and well-being of women. Also, Latin "juvenis" means "young people.")

Iulius (31 days) (Named after Julius Caesar)

Augustus (29 days) (Named after Augustus)

September (29 days) (Comes from the Latin work "septem" meaning "seven;" as is the case of October, it was once the 7th month of the year)

October (31 days) (Latin: octo means eighth)

November (29 days) (From the Latin: "novem" meaning "ninth")

December (29 days) (From the Latin: "decem" meaning "tenth")

The Missing Months and the Old Julian Calendar
Before the addition of Iulius and Augustus, the other two months were Quintilus and Sextilis (5th and 6th, respectively). The old calendar originally began in March, with January and February being the last months of the year.

So then, the old calendar was Marius, Aprilis, Maius, Iunius, Quintilis, Sextilis, September, October, November, December, Ianuaruis, and Februarius.

October means 8 ("octo"). Yet it is the 10th month in the calendar. This is because it was pushed forward due to the addition of two new months: Iunius and Augustus. Both of these months were named after emperors: Julius Caesar (he named the month after himself) and Augustus, respectively.

The second king of Rome, Numa Pompilius, caused the shift from March 1st as New Years to January 1st as New Years. This was roughly 700 years before Christ's birth.

In 44 B.C., Quintilis was renamed "Iulius" in honor of Caesar.

In 8 B.C., Sextilis was renamed "Augustus," in honor of Augustus.

Reckoning Days
In the Gregorian calendar, we simply say "Monday the 13th." The Gregorian calendar is a bit more complicated, as they count towards "reckoning days." There were three reckoning days each month, the "Kalends," which fell on the 1st day, the "Nones," which fell on the 5th day, and the "Ides," which fell on the 13th day of the month. The exception here is the four months with 31 days (Martius, Maius, Iulius, and October). Ides means "to divide." What do Kalend, Nones, and Ides mean? These months are pushed back by two days to account for the extra two days. Nones occur on Day 7 and Ides are on Day 15. (The Kalends still fall on the 1st of the month.) Julius Caesar was killed March 15, 44 BC. This is why people say he was killed on the "Ides of March."

Inclusive Counting
Instead of counting the days as we do in the Gregorian system, the Romans used "Inclusive Counting." This revolved around basing the date off of reckoning days. If you were counting from the 9th of Aprilis, it would be the 5th day from the Ides (the Ides fall on the 13th). If you are past the Ides of one month, you count to the Kalends of the next.

The say the date, you would begin with the phrase "Hodie est" (today is), followed by naming the day of the week, followed by a comma, followed by A.D. A.D. here doesn't mean "Year of our Lord." In this context, it is "Ante Diem," used to represent the days before the next reckoning day. A.D. is followed by the number of days until the next reckoning day, the reckoning day you're counting to, and the name of the month.

Note that the reckoning days are abbreviated here. Kalends, Nones, and Ides become Kal, Non, and Id. The months are also abbreviated here, as Ian, Feb, Mar, Apr, Maius, Iun, Iul, Aug, Sept, Oct, Nov, Dec.