Every new religion has its own calendar and the Bahá'í Faith is no different.
The year is based on the solar year of 365 days, five hours and some fifty minutes. Each year is divided into nineteen months of nineteen days each with four Intercalary Days (five in a leap year), called Ayyám-i-Há, which Bahá'u'lláh specified should precede the nineteenth month called 'Alá' (the month of fasting).
Ayyám-i-Há is devoted to spiritual preparation for the fast, hospitality, feasting, charity and gift giving.
New Year's Day (Naw Rúz) falls on the Spring Equinox in the Northern Hemisphere.
The Bahá'í day of rest is Istiqlál (Friday) and the Bahá'í day begins and ends at sunset.
The Báb divided the years following the date of His Revelation into cycles of nineteen years each.
Each cycle of nineteen years is called a Váhid. Nineteen cycles constitute a period called Kull-i-Shay'.
The names of the months in the Bahá'í (Badí) calendar were given by the Báb, who drew them from the nineteen names of God invoked in a prayer said during the month of fasting in Shí'ih Islam.

The Holy Days
Naw Rúz - March 21 (New Year)
First Day of Ridván - April 21 (Declaration of Bahá'u'lláh)
Ninth Day of Ridván - April 29 (Declaration of Bahá'u'lláh)
Twelfth Day of Ridván - May 2 (Declaration of Bahá'u'lláh)
Declaration of the Báb - May 23
Ascension of Bahá'u'lláh - May 29
Martyrdom of the Báb - July 9
Birth of the Báb - October 20
Birth of Bahá'u'lláh - November 12
Work does not have to cease on these Holy Days:
Day of the Covenant - November 26
Ascension of 'Abdu'l-Bahá - November 28

The Weekdays
1 - Jalál - Glory - Saturday
2 - Jamál - Beauty - Sunday
3 - Kamál - Perfection - Monday
4 - Fidál - Grace - Tuesday
5 - 'Idál - Justice - Wednesday
6 - Istijlál - Majesty - Thursday
7 - Istiqlál - Independence - Friday

The Days and the Months
1 - Bahá - Splendour - (21 March - 8 April)
2 - Jalál - Glory - (9 April - 27 April)
3 - Jamál - Beauty - (28 April - 16 May)
4 - 'Azamat - Grandeur - (17 May - 4 June)
5 - Núr - Light - (5 June - 23 June)
6 - Rahmat - Mercy - (24 June - 12 July)
7 - Kalimát - Words - (13 July - 31 July)
8 - Kamál - Perfection - (1 August - 19 August)
9 - Asmá' - Names - (20 August - 7 September)
10 - 'Izzat - Might - (8 September - 26 September)
11 - Mashíyyat - Will - (27 September - 15 October)
12 - 'Ilm - Knowledge - (16 October - 3 November)
13 - Qudrat - Power - (4 November - 22 November)
14 - Qawl - Speech - (23 November - 11 December)
15 - Masá'il - Questions - (12 December - 30 December)
16 - Sharaf - Honour - (31 December - 18 January)
17 - Sultán - Sovereignty - (19 January - 6 February)
18 - Mulk - Dominion - (7 February - 25 February)
Ayyám-i-Há - (26 February - 1 March)
19 - 'Alá - Loftiness - (2 March - 20 March)

The Years and the Váhid
1 - Alif - The Letter "A"
2 - Bá - The letter "B"
3 - Ab - Father
4 - Dál - The letter "D"
5 - Báb - Gate
6 - Váv - The letter "V"
7 - Abad - Eternity
8 - Jád - Generosity
9 - Bahá - Splendour
10 - Hubb - Love
11 - Bahháj - Delightful
12 - Javáb - Answer
13 - Ahad - Single
14 - Vahháb - Bountiful
15 - Vidád - Affection
16 - Badí - Beginning
17 - Bahí - Luminous
18 - Abhá - Most Luminous
19 - Váhid - Unity

Some Examples

Monday, 21^st April 1930 (before sunset):
The weekday of Kamál, the day of Qudrat, of the month of Jalál, of the year of Bahháj, of the Váhid of Báb, of the first Kull-i-Shay'
(3^rd weekday, 13^th day, 2^nd month, 87^th year, 11^th year of the Váhid, 5^th Váhid, 1^st Kull-i-Shay')

Sunday, 5^th April 1987 (after sunset):
The weekday of Kamál, the day of Sultán, of the month of Bahá, of the year of Bahháj, of the Váhid of Jád, of the first Kull-i-Shay'
(3^rd weekday, 17^th day, 1^st month, 144^th year, 11^th year of the Váhid, 8^th Váhid, 1^st Kull-i-Shay')

Wednesday, 27^th January 1988 (before sunset):
The weekday of 'Idál, the day of Asmá', of the month of Sultán, of the year of Bahháj, of the Váhid of Jád, of the first Kull-i-Shay'
(5^th weekday, 9^th day, 17^th month, 144^th year, 11^th year of the Váhid, 8^th Váhid, 1^st Kull-i-Shay')

Sunday, 14^th August 1988 (after sunset):
The weekday of Kamál, the day of Masá'il, of the month of Kamál, of the year of Javáb, of the Váhid of Jád, of the first Kull-i-Shay'
(3^rd weekday, 15^th day, 8^th month, 145^th year, 12^th year of the Váhid, 8^th Váhid, 1^st Kull-i-Shay')

Sunday, 20^th November 1988 (before sunset):
The weekday of Jamál, the day of Sultán, of the month of Qudrat, of the year of Javáb, of the Váhid of Jád, of the first Kull-i-Shay'
(2^nd weekday, 17^th day, 13^th month, 145^th year, 12^th year of the Váhid, 8^th Váhid, 1^st Kull-i-Shay')

Wednesday, 26^th April 1989 (before sunset):
The weekday of 'Idál, the day of Mulk, of the month of Jalál, of the year of Ahad, of the Váhid of Jád, of the first Kull-i-Shay'
(5^th weekday, 18^th day, 2^nd month, 146^th year, 13^th year of the Váhid, 8^th Váhid, 1^st Kull-i-Shay')

Saturday, 27^th December 1997 (after sunset):
The weekday of Jamál, the day of Sultán, of the month of Masá'il, of the year of Bá, of the Váhid of Bahá, of the first Kull-i-Shay'
(2^nd weekday, 17^th day, 15^th month, 154^th year, 2^nd year of the Váhid, 9^th Váhid, 1^st Kull-i-Shay')

Saturday, 18^th July 1998 (after sunset):
The weekday of Jamál, the day of Kalimát, of the month of Kalimát, of the year of Ab, of the Váhid of Bahá, of the first Kull-i-Shay'
(2^nd weekday, 7^th day, 7^th month, 155^th year, 3^rd year of the Váhid, 9^th Váhid, 1^st Kull-i-Shay')

Wednesday, 21^st March 2001 (before sunset):
The weekday of 'Idál, the day of Bahá, of the month of Bahá, of the year of Váv, of the Váhid of Bahá, of the first Kull-i-Shay'
(5^th weekday, 1^st day, 1^st month, 158^th year, 6^th year of the Váhid, 9^th Váhid, 1^st Kull-i-Shay')