One of the beauties of homeschooling is that families can set their own schedule. It is not necessary to follow a traditional school calendar, although many families do. Some parents find it works better to keep their kids on a year round schedule, others plan on taking time off when other family members have vacation time or to travel. Most states have requirements regarding the number of school days per year. In my state, North Carolina, students are required to attend school for 180 days per year. So, if you begin homeschooling in the middle of the school year, you can count the number of days the student attended traditional school prior to beginning homeschooling toward the required number of school days for that school year.
As far as curriculum goes, you may choose to continue work that the child began in traditional school or you may not. Each state has different curriculum requirements, so it is best to first check with your state's department of non-public education. The Homeschool Legal Defense League has a state by state guidelines chart.