The Silent Amidah
Also known as: [Shemoneh Esrei] (There are many different [transliteration]s.)

Amidah is a [hebrew] word which means stance approximately. It is called the Amidah because when at all possible, it is said standing.¹
Shemoneh Esrei is Eighteen in hebrew. Since hebrew [syntax] is somewhat reversed, the number eight(shemoneh) precedes the number ten(eser).

The Central Prayer
The Amidah is the central [prayer] around which all other Jewish prayer orbits. Often, in the [Talmud] and other halachic sources, when the word prayer is used, it is understood to mean the Amidah. For example the Talmud tells us that the [Chasidim HaRishonim], the early pious people, would meditate for an hour and then pray for an hour, and then finish up with a final hour of meditation.² The middle hour, in which they prayed was the time at which they said the Amidah. Everything else that [Jews] say [nowadays] during prayer (besides the Amidah) falls into the category of what was then considered meditation.

A Brief History of the Amidah
Up until the creation of the [Mishkan], the [Tent of Meeting] (aka. [Tabernacle]), Jews prayed whenever and wherever and whatever, at their own discretion. [Avraham] prayed in the mornings. [Yitzhak] in the afternoons and [Yaakov] in the evenings, for example.³

From the time of the Mishkan until the fall of the [First Temple], there were two [Karbon Tamid|Tamid] offerings brought daily in the name of the Israelite nation. At this point the Jews were exiled. When they returned (6th century [BCE]) to build the [Second Temple] the Rabbis of the [Great Assembly], [Anshei Knesset HaGedolah], along with [Ezra the prophet], established the text, the structure of the Amidah. This was done so that people who did not know how to phrase their own prayers could still pray together.

After the destruction of the [Second Temple] the Rabbis established set times for prayer, to commemorate the services in the [Beit HaMikdash], the Holy Temple. The morning prayer commemorates the morning offering. The afternoon prayer replaced the afternoon offering. The evening prayer represented the flesh of the earlier offerings that burned on the altar throughout the night. Since then, the structure of the Amidah is for the most part unchanged.⁴

Timing of the Amidah
According to [Orthodox] Judaism:

Men are required to recite the Amidah three times a day. Morning ([Shacharit|Shaharith]), Afternoon ([Mincha|Minha]), and Evening ([Arvith]/[Maariv]).
An additional ([Musaf]) Amidah is recited on Shabbath and Holidays ([Yom Tov]). This Amidah is generally said between Shaharith and Minha. All the days in which the Musaf is added are as follows:
1. [Shabbath] ([Sabbath])
2. [Rosh Hodesh] ([New Month])
3. [Rosh HaShana] ([Jewish New Year])
4. [Yom Kippur] ([Day of Atonement])
5. Eight days of [Sukkoth] ([Feast of Tabernacles])
6. Seven days of [Pesah] ([Passover])
7. [Shavuoth] ([Pentecost])
[Tefillin] are not generally worn during Musaf, even on days where they are worn for shaharith.
[Tashlumim], an additional Amidah can be said immediately following an Amidah after one which was missed. An example will make this a little more clear: If one missed an Amidah, let us say Shaharith, Then, immediately after the Minha Amidah, one could say a Tashlumim Amidah to make up for the missed Shaharith Amidah. If one did not realise they missed Shaharith until two Amidahs later, until Arvith, a Tashlumim cannot be said.
A [Nedava], a voluntary Amidah can be said at any point in time, but this is rarely done. It is better to express one's prayers within the structure set up by the Rabbis.⁵
The [Ne'ila], "locking", is a special additional Amidah recited only at the very end of [Yom Kippur].
It should be noted that [Women] are required to pray only once daily, at no specific time, because women are not required to perform any positive [mitzvah|mitzwoth] (commandments) which are bound by time constraints. Women can take all the Amidahs upon themselves as an obligation. This is inadvisable simply because once you take it upon yourself, you cannot freely give it up. If you miss one Amidah it is as if you have broken an oath to God, which is pretty extreme, spiritually speaking. It is better, just as is the case with the Nedava Amidah, to express your prayers in the established prayer times than to worry about adding to your already stringent obligations. However, [always consult your Rabbi] for personally pertinent Halachic issues.

[Structure] of the Amidah
The Amidah is normally made up of nineteen blessings. Each blessing has an introductory sentence or two and then a final Hatima, simple blessing, that seals the larger blessing. The seals (final words) of the blessings are as follows: (It is my hope I will get a chance to node all of these blessings with their complete texts and some of their deeper meanings. [iy"h])

The first three blessings are said to be in recognition of [God's grandeur].
1. [Magen Avraham] - He protects Avraham.
2. [Mehayye Maytim] - He gives life to the dead.
3. [HaKel HaKadosh] - He is Holy.
The second group of blessings, normally the middle thirteen, represents our [national] and [personal] requests and desires. These middle blessings are replaced with a single blessing on Shabbath and holidays.
1. [Honen HaDaath] - He graces with [knowledge].
2. [HaRotzeh bTeshuva] - He wants repentance.
3. [Honen HaMarbeh lSloah] - In his [graciousness] he [forgive]s constantly.
4. [Goel Yisrael] - He [redeems] Israel.
5. [Rophe Holei Amo Yisrael] - He [heals] our ill.
6. [Mevarech HaShanim] - He blesses the years.
7. [Mekabetz Nidhey Amo Yisrael] - He gathers [exiles] of Israel.
8. [Melech Ohev Tzedaka uMishpat] - He loves [righteousness] and [justice].
9. [Shover Oyvim uMachnia Zeydim] - He breaks our [enemies] and diminishes our [foes].
10. [Mishaan uMivtah laTzaddikim] - He supports and provides surety for the [pious].
11. [Bonei Yerushalayim] - He builds [Jerusalem].
12. [Matzmiah Keren Yeshua] - He blossoms the [ray] of [redemption].
13. [Shomea Tefilla] - He hears prayers.
The last three blessings are said to represent our giving thanks to God for all that he gives us.
1. [HaMahazir Shechinato lTzion] - He returns his [Divine Presence] to [Zion].
2. [HaTov Shimha uLcha Naeh lHodoth] - His name is good and pleasant to thank.
3. [HaMevarech eth Amo Yisrael baShalom] - He blesses his people Israel with [peace].

Rules Regarding Recitation of the Amidah

Before beginning the Amidah you take three steps backward, and take three steps forward while saying "Adonai sifatai tiftah (God, open my lips) u'phi yagid tehilatecha (That my mouth utter your praises)"
One should try to maintain four [Amoth] ([cubit]s)⁶ of space between oneself and other people also reciting the Amidah. This only applies in an open space, but if there is some furniture or wall between you and any other people, they may be closer than four amoth.
It is proper to stand while reciting the Amidah.
It is called the silent Amidah because the words are to be mouthed but not voiced.
We bow four times throughout the course of the Amidah:
1. At the beginning of the first [beracha](blessing), we bow at the neck with the word "baruch", and at the waist with the word "atah", and straighten before saying God's name.
2. The second bow takes place at the end of the first blessing, the same way with the same words.
3. The third bow is special in that it is a deeper bow, and coincides with the words "modim anahnu lach," the beginning of the eighteenth blessing.
4. The fourth and final bow is like the first two and occurs at the end of the eighteenth blessing with the words "baruch" and "atah" and God's name.
After you have completed the Amidah, you take three steps back with your head bowed. In the event that you are praying in less than four amoth of space, it is a good idea to pray in a place with at least three steps of space behind you, so you can back up appropriately. Then you bow first to the left (Which is the right of the [Shechina] which you are facing.) saying "Oseh shalom b'm'romaw." (He makes piece in His high places) Then you bow to the right (which is the left side of the [Divine Presence]) saying "Hu b'rahamaw yaaseh shalom aleinu." (In his mercy He will make peace upon us) Lastly you bow straight ahead saying "Aleinu w'al kol yisrael w'imru amen." (Upon us and all of Israel, and we say amen.) It is said that the three steps that we take backwards at the end of the Amidah are taken to undo the three steps that the destroyer of the holy temple rushed forward to destroy it.
If someone is standing in your way and is still reciting the silent Amidah, wait till he finishes before taking your three steps back and concluding your own Amidah.
After all of the Amidahs except the Arvith (Evening) prayer, the [Shaliah Tzibur] (the "messenger of the congregation", aka. the [cantor]) recites the Amidah aloud, after the silent recital, with the inclusion of the [kedusha]. In the morning Amidah some ([Sepharadi] and [Yerushalmi]) congregations also include the [Birkath Kohanim], the [Priestly Blessing].

1. The [halacha|major halachic works] discuss how [in extremis] the Amidah can be said sitting down, or even riding on the back of a camel.
2. They did this three times a day.
3. Yitzhak (aka. [Isaac]) also prayed in the morning, following the traditions of his father. Yaakov (aka. [Jacob]) prayed in the mornings and the afternoons as well, following his father Yitzhak's example in maintaining the traditions of the previous generations.
4.There is one exception, the addition of the nineteenth blessing.
5.The Amidah contains nineteen blessings and it is not our practice to say blessings lightly. Each blessing contains at least one mention of God's name and we try especially hard never to utter God's name in vain.
6.A cubit is the distance from your elbow to your finger tip. About a foot and a half. So, four cubits is about six feet. Perhaps a little less.

I'm probably going to take a lot of flack on the transliterations. If someone has a more consistent or more popular transliteration method please let me know. I tried to transliterate the way I speak the words, with consistant spellings as well.

sources beyond my own memory:
http://freespace.virgin.net/family.sedley/5CHAYEI59.htm
http://coavoice.com/amidah.htm
http://www.ohrtorah.org/nov.html

sources from my memory: [Ben Ish Hai], [Yalkuth Yosef], [Shulchan Aruch], [Mishna Berurah]

Amidah (thing)