The Islamic Calendar is 'Al-Taqweem al-Islami' in Arabic - it is often called the 'Hijri' Calendar because it is started from the 'Hijrah' (migration) of the Muslims from Makkah to Madina to escape persecution. This occurred in the year 620/621AC, so the current year 2008CE is 1429AH. AH means 'after hijrah'.
There are 12 months in the Islamic calendar and the names of these months are:

1. Muharram
2. Safar
3. Rabi` al-Awal
4. Rabi` al-Thani
5. Jumadal-awal
6. Jumadal-thani
7. Rajab
8. Sha`ban
9. Ramadhan
10. Shawwal
11. Dhul Qi`dah
12. Dhul Hujjah

The calendar is based on the movements of the phases of the moon so it does not correlate perfectly with the Gregorian calendar which is based on the sun. There are 354 days in the lunar year (as a pose to 364 days in the solar year) and the Islamic months tend to start 10/11 days earlier than the solar year before so the start of the month is always changing - if the month of Ramadhan last year started on the 11th of October, we should expect it to start on the 1st of October next year.