First Day (and 2nd day in the Diaspora)

Evening service ( Ma'ariv )

As on any festival (similar to Shabbat).
If Shabbat, preceded by an abbreviated version of Kabbalat Shabbat.

Morning service ( Shacharit )

As on any festival (partly similar to Shabbat), until the amidah, which is for Succot.
After the amidah the arba'ah minim are taken and the full Hallel is said. (On Shabbat the arba'ah minim are not taken.)
In some congregations, after Hallel the Hoshana prayers are said (instead of in additional service – see below).
In Israel, if on Shabbat, Megillat Kohelet (the Scroll of Ecclesiates) is read.
The main Torah reading is Leviticus 22:26 – 23:44. (Both days in the Diaspora).
Five people are called up to the Torah (seven on Shabbat).
The Maftir is Numbers 29:12-16. (Both days in the Diaspora).
The Haftarah is Zechariah 14 on the first day; I Kings 8:2-21 on the second day (in the Diaspora).

Additional service ( Mussaf )

The Succot amidah : Only the sacrifice for the first day is mentioned (in the Diaspora, even on the second day).
After the amidah , the Hoshanot are said (including Shabbat), taking the arba'ah minim (except on Shabbat) and circling the bimah once. In some congregations this is done after Hallel (see above).

Afternoon Service ( Minchah )

As on any festival. If Shabbat, there is Torah reading.

Chol Hamo'ed (except Shabbat)

First Evening

After the evening service, Havdalah is said, without the preamble, without spices and without the candle (unless it is also the end of Shabbat).

Morning Service Shacharit (each day, except Hoshanah Rabbah)

Regular morning service. ( Yaaleh veyavo included in the amidah ).
In the Diaspora, where tefillin are worn: After the amidah, the tefillin are removed.
The arba'ah minim are taken, and full Hallel is read, (followed by the Hoshana prayers, if recited after Mussaf ).
Torah reading from Numbers 29, to which four people are called up. (In Israel, one section, different each day, is read four times; in the Diaspora it is more complicated).

Additional Service Mussaf (each day except Hoshana Rabba)

The Succot amidah, including the sacrifice for the day in question (in the Diaspora also for the day before), followed by a single circuit of the central platform with the arba'ah minim while saying the Hoshanot (unless these were said during Shacharit).

Hoshanah Rabbah

As on the other days of Chol Hamo'ed, except that extra Psalms are said in the early part of Shacharit (as on Shabbat and Festivals); there are seven circuits instead of one for the Hoshanot, in which the arba'ah minim are replaced at the end by the bunch of aravot (willows).

Shabbat Chol Hamo'ed

Evening Service (Ma'ariv)

As on an ordinary Shabbat (including Yaaleh veyavo in the amidah).

Morning Service (Shacharit )

As on ordinary Shabbat (including Yaaleh veyavo in the amidah).
The arba'ah minim are not used.
After the amidah the full Hallel is said. (This is followed by the Hoshana prayers by those who do not say them after the additional service).
Megillat Kohelet (Scroll of Ecclesiates) is then read.
The main Torah reading is Exodus 32:12 – 34:26.
The Maftir is taken from Numbers 29 (depending on which day of the festival it is).
The Haftarah is Ezekiel 38:18 – 39:15, the story of the war of Gog and Magog. (Note that Gog is the king of Magog; they are not, as popularly supposed, two people fighting each other, despite the famous statue!).

The final blessing of the Haftarah mentions both Shabbat and the Festival (unlike the intermediate Shabbat of Pesach, where only the Shabbat is mentioned).

Additional Service (Mussaf)

The Succot amidah (with Sabbath insertions), followed by Hoshanot (unless said after the morning service).

Afternoon Service (Minchah)

As on an ordinary Shabbat (including Yaaleh veyavo in the amidah ).