How do Jews celebrate the feast of first fruit these days?

Answer 1

I had to do some real searching because 'feast of first fruits' is a Christian term. The holiday is actually called Shavu'ot.

Shavu'ot is celebrated by staying awake all night studying Torah and preparing to receive the Torah anew the next morning.

This is also the only holiday where traditionally only dairy foods are eaten. The reason being that as the Torah was received, we were now obligated to keep kosher. Since there were no kosher utensils to slaughter animals and cook them, dairy was eaten instead.

Answer 2

The Sabbath and all of the festivals are "in remembrance of the Exodus from Egypt" (Kiddush prayer). But more than any other occasion or observance, it is Passover that has reliving the Exodus as its entire essence.

In Pesach (Passover) we relive the Exodus from Egypt and our birth as a nation, both of which were preparations for receiving the Torah from God.
The highlight of Passover is the Seder meal. This meal is of great importance in Judaism. It is a 3325-year old continuous tradition that began on the night of the Exodus from Egypt (see Exodus chapter 12), and is fully detailed in our ancient Oral Traditions (Talmud, chapter Arvei Pesachim).
The Seder meal is one of those occasions, like Yom Kippur and Hanukkah, that Jews all over the world, Orthodox and non-Orthodox alike, observe in common. During the Seder, we keep the essential mitzva and customs of handing Jewish traditions down to the next generation, with the traditional Seder foods and the ceremony of reading the Passover Haggadah which retells the events of the Exodus.
During the Seder meal, other traditional foods are eaten in addition to the matzah: bitter herbs, parsley, wine and haroset (see below). Salt water, a roasted egg, and a bit of roasted meat are also on the table.
During all the days of Passover, matzah (unleavened bread) is eaten; while leavened foods such as bread, cake, cookies, cereal and pasta are forbidden. Certain prayers are added in the synagogue services, and the Torah is read each day.
Here is the symbolism of the items on the Seder plate:
The bitter herbs (maror) symbolize the harsh slavery which the Israelites suffered in Egypt. Either horseradish or romaine lettuce is traditionally used for maror.
Charoset - A sweet mixture representing the mortar used by the Jewish slaves to build the storehouses of Egypt. In Ashkenazi Jewish homes, charoset is traditionally made from chopped nuts, grated apples, cinnamon, and sweet red wine.
Karpas - A vegetable other than bitter herbs, traditionally parsley, which is dipped into salt water at the beginning of the Seder. The dipping of a simple vegetable into salt water (which represents tears) recalls the pain felt by the Jewish slaves in Egypt.
Beitzah - A hard-boiled egg, symbolizing the korban chagigah (festival sacrifice) that was offered in the Temple in Jerusalem and roasted and eaten as part of the meal on Seder night. Although both the Pesach sacrifice and the chagigah were meat offerings, the chagigah is commemorated by an egg, a symbol of mourning.
Z'roa - A roasted lamb or goat shank-bone, chicken wing, or chicken neck; symbolizing the korban Pesach (Pesach sacrifice), which was a lamb that was offered in the Temple in Jerusalem, then roasted and eaten as part of the meal on Seder night.

Answer 3

1) We hold the Passover Seder, a special festive meal at which the Exodus is recounted at length, with ceremonial foods, narrative and songs

2) We refrain from work on the days in which work isn't allowed

3) We pray the Festival prayer-services in the synagogue, and the Torah is read

4) We eat matzoh instead of bread; and no leavened products are eaten or purchased during Passover.

See also Exodus ch.12.