Apples and Honey:

• A slice of apple is dipped in honey.
• The blessing for the fruit of the tree is recited:

Baruch atah Ado-nai, Ehlo-haynu melech Ha-olam, Borai p'ree ha'aitz.

Blessed are you L-rd, our G-d ruler of the world, Creator of the fruit of the tree

• Take a bite and then recite the following brief prayer:

May it be Your will, Hashem, our G-d and the
G-d of our forefathers, that
You renew for us a good and sweet year.

Dates
(t'marim - from the word for "to consume")

"May it be Your will, Hashem, our G-d and the G-d of our forefathers, that our enemies be consumed."

• some people eat the date first because it is one of the fruits for which the Land of Israel is known.

Squash
(kara - from the word for "to tear")

"May it be Your will, Hashem, our G-d and
the G-d of our forefathers, that the decree of our sentence be torn asunder; and may our merits be proclaimed before You."

Black-eyed Peas
(rubia - from the word for "increase") or
Carrots
(merrin, in Yiddish - from the word "more")

"May it be Your will, Hashem, our G-d and the G-d of our forefathers, that our merits increase."

Raisins and Celery
(this is a recent, somewhat humorous, English addition)

"May it be Your will to grant us a "raise in salary."

Pomegranates

• It is said that each pomegranates has 613 seeds, representing the 613 commandments of the Torah:

"May it be Your will, Hashem, our G-d and the G-d of our forefathers, that our merits be as plentiful as the seeds of a pomegranates.

Fish

• A fish is considered to be a symbol of fertility and blessing:

"May it be Your will, Hashem, our G-d and the G-d of our forefathers, that we be fruitful and multiply like fish."

Head of a Sheep/Fish:

• Some have a custom to have the head of a sheep or a fish on the table and to say:

"May it be Your will, Hashem, our G-d and the G-d of our forefathers, that we be as the head and not as the tail

Nuts

On Rosh Hashana, nuts are not eaten since the numeric value of the word for nut, egoz, is equivalent to the numeric value for the word for sin, chet.