The easiest way to determine the week of the year is to enter the date into an online calculator such as whatweekisit.com. However, using knowledge of the Gregorian calendar and some basic math, one can determine the week of the year without outside help.
Any online week-of-the-year calculator eliminates the need for calculations, but the steps to determine the week of the year are simple. While the first day of the first month of the year varies from year to year, the first day of the week is always Sunday. Look at a calendar, beginning at January of the year in question and find the first Sunday of that year, then count each successive Sunday until the week under consideration.
Another way to determine the week of the year is to determine the day of the year, calculating how many days it has been since the first day of the year. Some calendars provide this information. Divide that number by seven to determine how many weeks have passed that year. This answer may vary slightly from the counting method because it doesn't take into account full calendar weeks, simply seven-day periods. However, the difference between the two methods is a maximum of seven days.