Each month should start with the first visible appearance of the new moon but this has its problems. Firstly it will be affected by factors such as how close the moon is to the sun as viewed by the observer, the relative brightness of sun and moon, weather conditions, and pollution. Secondly the day on which the new moon becomes visible depends on the position of the observer. Some Muslims prefer to use their own start to the month based on their own observation, while others will depend on an announcement by a person in authority. These factors mean that it cannot be predicted in advance. Because of this the first visible appearance of the new moon is used only for religious purposes. For civil purposes the calendar is based on calculated new moons. If there is poor visibility and the moon is not visible for several nights then a new month will always start no later than 30 days after the previous month started. Note that the month starts in the evening of the last day of the month, not at midnight.
The days of the week are not named but numbered. They are sometimes written as a word but this is just the number spelled out.
The names of the months are -
3. Rabi' al-awwal (Rabi' I)
4. Rabi' al-thani (Rabi' II)
5. Jumada al-awwal (Jumada I)
6. Jumada al-thani (Jumada II)
9. Ramadan (the month of fasting)
11. Dhu al-Qi'dah
12. Dhu al-Hijjah
As these names are translated from the Arabic other spellings are possible.
Years are counted since the Hijra, that is, Mohammed's flight to Medina, which is assumed to have taken place on Friday 16th July 622 AD (Gregorian calendar). On that date AH 1 started (AH = Anno Hegirae = year of the Hijra, or 'going away'). For comparison the 1st January 2000 AD was 24th Ramadan 1420.
The Islamic calendar does vary from country to country. This is because of
the lack of a standard definition of 'first visibility' and the fact that
different countries are at different positions on the globe. Some of the
variations are as follows -
Singapore - On the evening of the 29th day a new month will start if the moon is more than 2 degrees above the horizon. Otherwise the new month starts at the end of the 30th day.
Egypt - A new month will start if moonset is at least 5 minutes after sunset.
Saudi Arabia - Saudi Arabia doesn't rely on a visual sighting of the crescent moon to fix the start of a new month. Instead they base their calendar on calculations. Since 1999 (1420 AH) the rule has been as follows: On the 29th day of an Islamic month, the times when the sun and the moon set are compared. If the sun sets before the moon, the next day will be the first of a new month; but if the moon sets before the sun, the next day will be the last (30th) of the current month. The times for the setting of the sun and the moon are calculated for the co-ordinates of Mecca.