The instruction concerning the Feast of Unleavened Bread, that I have found so far in Scripture, is as follows:
It is to be perpetually kept as a memorial of our deliverance from Egypt (Exo 12:14, 17; Exo 23:15; Exo 34:18; Deu 16:1-3), and we shall tell our children why we are observing the feast, and how the Lord delivered us from Egypt (Exo 13:8).
The native born as well as the foreigners among them shall keep it (Exo 12:19).
It shall last for seven days during which time we eat unleavened bread, and whoever eats anything leavened for the duration of the feast will be cut off from Israel (Exo 12:15, 18-20; Exo 13:6-7; Exo 23:15; Exo 34:18; Lev 23:6; Num 28:17; Deu 16:1; Eze 45:21).
The seven days of the Feast will be from the 14th through the 21st days of the first biblical month (Exo 12:18; Exo 23:15; Lev 23:5-6; Num 28:16-17; Eze 45:21).
Leaven shall be removed from our dwelling on the first day, and no leaven shall be found in our houses for the seven days of the Feast (Exo 12:15, 19; Exo 13:7; Deu 16:4).
The first and seventh days are sabbaths of rest, in which the believers gather together to worship the Lord (Exo 12:16, Lev 23:7-8; Num 28:18, 25; Deu 16:8) culminating with a feast to the Lord on the seventh day (Exo 13:6).
We may not do ordinary work on the first and seventh day sabbaths, but food for that day may be prepared (Exo 12:16; Lev 23:7-8; Num 28:18, 25; Deu 16:8).
We shall offer to the Lord an offering made by fire for seven days for each day during the feast (Lev 23:8; Num 28:19-24, see the living olah for the practical application).
Should Christians keep the Feast? Paul instructed them to:
Your glorying is not good. Do you not know that a little leaven leavens the whole lump? Therefore purge out the old leaven, that you may be a new lump, since you truly are unleavened. For indeed Christ, our Passover, was sacrificed for us. Therefore let us keep the feast, not with old leaven, nor with the leaven of malice and wickedness, but with the unleavened bread of sincerity and truth. 1 Cor 5:6-8
The Corinthians were Greeks, Gentiles. Why would Paul be telling Greeks to celebrate Jewish feasts? Because the feast days are not the feasts of the Jews, but the feasts of the LORD (Lev 23:1-2). These Greeks had come into the worship and service of the LORD God, Creator of heaven and earth, just as we have done.
But his application for them was this: let us not merely keep the outward rituals, but let us take this time to purge the sin from our hearts just as diligently as we purged the leaven from our houses, so that we are partaking of the unleavened bread of sincerity and truth.
Further reading on celebrating the feasts:
the feasts of the Lord (collection of articles including Passover)
observing unleavened bread
holy convocations, nehemiah 8-9
the living olah (the sacrifice made by fire)
the Lord’s supper, 1 corinthians 11
Israel’s Feasts and Their Fullness by Batya Wooten
Christine’s incomplete menus and recipes for Unleavened Bread (I am learning too!)