On the second night of Passover, religious Jews begin counting something known as Sefirat Haomer or “The Counting of the Omer”. Beginning on the first night from number one, we count all the way up to 49. We call the fiftieth day Shavuos, a Jewish holiday where we celebrate receiving the Torah. Sefirat Haomer is, essentially, a form of counting until the day we receive the Torah. It’s a way to express our excitement and anticipation, just as a bride would count down towards her wedding day.
(As a bit of background, “Omer” is a measurement used in the times of The Temple. It alludes to a sacrifice containing an omer-measure of barley. This sacrifice was offered up until Shavuos, when a wheat-offering was brought instead. Therefore, we call it “The Counting of the Omer”: we are counting all the days that an omer of barley was brought , up until Shavuos. Because on Shavuos, the first day that a wheat offering was brought, we received the Torah.)
We can also use this time period of seven weeks to prepare spiritually, and cleanse ourselves. After all, we must be on a high level to be worthy of receiving the Torah.
As soon as it is nighttime (thirty minutes after sundown), one can verbally count sefirah. We also say a special blessing before actually counting.
You can find a Sefirat Haomer chart here. The chart includes the blessing that we say before counting, as well as a clear chart of exactly what you should be saying each night. It’ll even direct you to the option of signing up for email reminders each night!