The moed of Reishit Qatzir [beginning of the harvest] has almost no traditions.

The crop that is historically associated with the first fruit offering is barley.  It was usually planted towards the end of the year before the winter rains.  It grew, matured, and was ready to harvest in the spring, about the time of Passover.

 

Day after which Sabbath?

In the days of the Master, there was some debate about the meaning of "on the day after the sabbath" in Leviticus 23:11.  Was it referring to the weekly (Saturday) Sabbath, or was it referring to the first day of the Feast of Unleavened Bread (which is also a Sabbath rest day)?

The Sadducees (predominantly Levitical priests) chose the day after the weekly Sabbath: "Sunday" today.

The Pharisees (predominantly rabbis who were not priests) chose the day after the first day of Chag HaMatzot.  Since the Pharisees formed the core of what was to become Orthodox Judaism, Orthodox groups today use the fixed day of Nisan 16 (Nisan 14 was Pesach, Nisan 15 began Chag HaMatzot (a Sabbath), and Nisan 16 became Reishit Qatzir celebrating the feast of the first fruits of the harvest). 

Other groups held to the Sadduceean standard of the first day of the week (i.e., Sunday) after the Sabbath that occurred during the week of the Feast of Unleavened Bread.  Some early groups of believers followed this standard since it was the first day of the week when the empty tomb was discovered and the risen Messiah became known.

The debate between groups of believers regarding this topic was probably in Paul's mind when he penned Romans 14:5.  Until Messiah Yeshua returns to settle the debate, we will likely have no definitive answer.

Given the dispersion of the Israelites from their Land until the 20th century and the lack of a Temple, this particular moed has diminished in importance and observance.  A quick search of Jewish calendars and holy day descriptions on various Jewish websites show little or no information about this moed other than to mark the beginning of the "counting of the omer".  No special prayers or prayer services have been instituted, no special foods, and no special events or activities have been formed to mark this special day.

It's almost as if unbelieving Jews, in their denial of Yeshua as the Messiah and His death and resurrection as the "first fruits of those who are asleep", have ignored the moed which speaks the most about Him and His resurrection.  This is not a condemnation of them because G-d, Himself, has blinded their eyes so that the fullness of the Gentiles might be brought in (John 12:40, Romans 11:25).

May Messiah return quickly and bring in the complete harvest of His people!