Counting of the Omer begins on the evening of April 20, 2019
Pentecost/Shavuot begins evening Saturday June 8, 2019 and ends the following evening. Extending it another day, 24 hours to the following sundown is part of the Jewish tradition.
Behold, I (YAHUSHUA ha MASHIACH) send the Promise of MY FATHER upon you; but tarry in the city of Jerusalem until you are endued with power from on high.
But the Comforter, who is the RUACH ha KODESH, whom the FATHER will send in MY name, SHE shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
In Biblical times, on the morning of 16 Nisan (the morning after the Passover high shabbat of 15 Nisan), the sheaf/omer of the firstfruits of the barley harvest (Reshit Katsir literally Start of the Harvest) was waved and offered along with a male lamb as a burnt offering, and unleavened bread, oil and wine (Lv 23:9-16). This also starts the Sefirat HaOmer, Counting of the Omer, counting 7 weeks to Shavu'ot/Pentecost.
In modern times, the Jewish tradition is to start the counting at the start of the Jewish day, which starts in the evening—in otherwords, we begin the counting of the omer in the evening as 15 Nisan ends, and 16 Nisan begins. If you miss a night of counting, you can always do it the following morning, or before the next Jewish day begins.