When to pray?

The 5 Daily Prayers
Each of these are comprised of two types of prayer, obligatory (Fard) and non-obligatory (Sunnah). It is the Fard prayers that form the second pillar of Islam (Salat) as these are the ones that must be performed five times a day. The Sunnah prayers are optional and can be offered either before or after the Fard prayers depending on the time.

The times of each prayer depends greatly according to latitude. Muslims living on or near the equator experience very little variation in their prayer timetable, whereas Muslims living further away from the equator experience more variation (the city I live in lies at around 51º latitude, so we experience a moderate amount of variation). For more details, ask your local mosque or consult Islamicity's Prayer Timetable Calculator.

The timing and composition of each prayer is as follows (I have used my local prayer times as an example):

Fajr
This begins at dawn and ends just before sunrise. Here in Cardiff (UK), times for Fajr vary between 2:50am to 4:54am in midsummer, and 6:38am to 8:18am in midwinter. Fajr prayer consists of two Rak'at as Fard and two Rak'at as Sunnah (Rak'at = units of prayer: these are explained on the How to Pray page).
Zuhr
This begins just after the sun reaches it's zenith and ends in mid-afternoon. Here, the timing for the start of this prayer varies very little, taking into account clocks being put back or forward an hour for daylight savings (where applicable). It consists of four Rak'at as Sunnah, four Rak'at as Fard, then two more Rak'at as Sunnah.
'Asr
This begins at mid-afternoon and ends just before sunset. Here, the timing for the start of this prayer varies between 2:13pm in midwinter and 5:41pm in midsummer. It consists of four Rak'at as Sunnah followed by four Rak'at as Fard.
Maghrib
This begins just after sunset and ends at nightfall. Here, the timing for the start of these prayers varies between 4:10pm in midwinter and 9:39pm in midsummer. Maghrib consists of three Rak'at as Fard followed by two Rak'at as Sunnah.
Isha
This begins at nightfall and extends thorough to Fajr the following morning. Here, the start times for this prayer varies between 5:50pm in midwinter, to 11:00pm in midsummer. It consists of two Rak'ats, as sunnah, four Rak'at as Fard, then two Rak'at as Sunnah.
Friday (Jumu'ah) Prayers
The Jumu'ah prayer occurs every Friday around the same time as the Zuhr prayer, which it replaces. It is a congregational prayer (similar to a Sunday church service) which is obligatory on every man who is able to attend. Reasonable excuses for not attending would be travel or illness; in any case Zuhr prayer must be offered as soon as possible as a substitute. Women can attend if they want to, providing they have their husband's permission and there are adequate facilities at the mosque.

After the Adhan (call to prayer) is sounded, the Imam will begin his Khutba (sermon). This is given in two parts with a short break halfway, and can be in any language or languages. It usually lasts around 20-30 minutes and can cover general affairs currently concerning muslims, lessons from the Qur'an or Hadiths (sayings of the Prophet Muhammad, peace and blessings be upon him), or emphasizing basic aspects of our religion, such as the dangers of gambling or the importance of prayer.

After the Khutba is finished, the Imam leads the congregation in a two Rak'at prayer, which is sometimes followed by an appeal for charity or a funeral (Janazah) prayer.

Notes on Friday Prayers
Try to arrive for Friday prayers as early as possible, to ensure that you are sitting as close to the front as possible and to avoid disturbing those already listening to the Khutba.
It is good practice to take a bath beforehand, and to attend the prayer wearing clean, smart clothes.
Once the Khutba has begun, it is haram (forbidden) to greet or speak to others in the main prayer hall until the prayer is finished.
It is Sunnah to offer two or four rak'at of prayer after the adhan has sounded (before the khutba begins), and two rak'at after the main prayer has finished. However, these are optional and can even be offered at home.
Eid Prayers
Eid occurs twice a year; at the end of Ramadan (Eid-ul-Fitr) and on the last day of Hajj (Eid-ul-Adha). Eid prayers occur on the morning of the first day of each of these three-day festivals, usually around 9:00am. Eid prayers are obligatory for every man who can attend, and they cannot be substituted or made up later.

The prayer begins with the Imam leading the congregation in a two Rak'at prayer. However, a number of takbirs (raising the hands up to the head and saying Allahu Akbar - Allah is Greatest) is performed before each Rak'ah begins.

After the prayer, the Imam gives a khutba similar to that given on Fridays. However, the subject of the khutba is either the importance of giving Zakat (for Eid-ul-Fitr) or the importance of sacrifice (for Eid-ul-Adha - it is customary to sacrifice a sheep or cow on this day so that it's meat can be distributed to the poor).

An Important note on Eid Prayers
Try to arrive at the mosque for the Eid prayer AT LEAST 30 minutes before it is due to start. This is especially important as the mosque will get very crowded, and (depending on the size of the mosque) you may end up praying in the street!
Funeral (Janazah) Prayers
These are said in a congregation, but only need to be offered by some of the people present. It is not obligatory to offer these prayers yourself if there are others already doing so, but offering Janazah prayers carries a great reward.

Those offering the prayer stand in straight rows, as in normal prayers. The prayer itself consists of four Takbirs (raising the hands up to your ears and saying Allahu Akbar, Allah is greatest). After the first takbir, one quietly recites Surat Al-Fatihah (the first chapter of the Qur'an - select link to open PDF, or right-click and select 'Save As...'). After the second takbir, the Salat An-Nabi is read quietly (select link to open PDF, or right-click and select 'Save As...'). After the third takbir, one offers a suitable supplication for the deceased *, followed by the fourth takbir and offering peace greetings (Assalamu Alaikum - peace and blessings be upon you) over the right and left shoulders.

* One such supplication is:

Allahummaghfir lihayatina wa mayatina wa saghirina wa kahirina wa zhakirina wa unthana. Allahumma man ahyatahu minna fa-ahyahu 'alal Islam wa man tawafthu minna fa-tawafthu 'ala iman. Allahumma la tahrimna ajrahu wa la tudalana ba'dahu.

"O Allah! Forgive our living, our dead, our young, our old, our males and our females, those of us who are present, and those who are absent. O Allah! Whomsoever among us You keep to live, make him to live in Islam, and whomsoever You cause to die, let him die in faith. O Allah! Do not deprive us of our reward for (supplicating for) him, and cause us not to go astray after him.

This can be recited in Arabic, English or any language.

Tarawih Prayers
Tarawih prayers are held during the nights of Ramadan. They are offered in congregation in a mosque, usually immediately after Isha prayers have been completed. The entire prayer lasts for twenty-one Rak'at offered two at a time, although it is only necessary to pray a minimum of eight.

Although it isn't obligatory to attend Tarawih, it is extremely good practice to do so as prayers during the nights of Ramadan carry a great reward, especially those offered on Lailat'ul Qadr (the night that the first ayat of the Qur'an was revealed to Muhammad (peace and blessings be upon him).

Other Prayers
Prayers can be offered at virtually any time of the day. Good times to pray are mid-morning (Duha), during the last third of the night (Tahajudd), and during heavy storms, droughts and eclipses