The US has no federal law that requires employers to give paid vacation, paid holidays or (for most private jobs) paid sick days. What you get depends on your employer and your state.
PTO (paid time off): one bank of days for vacation and sickness. Many office jobs start at about 10 to 15 days a year, plus holidays, and increase with years of service.
Paid holidays: often 6 to 11 days, such as New Year's Day, Memorial Day, July 4, Labor Day, Thanksgiving and Christmas.
Days are often accrued (earned little by little) each pay period. In your first months you may have only a few days.
Some companies have "unlimited PTO", which really means "ask your manager".
Read your offer letter and the employee handbook. Ask HR: "How many PTO days do I get, and do unused days roll over or get paid out?"
Many states and cities require employers to give paid sick leave, often about 1 hour for every 30 hours worked. Others require nothing. This differs by state; see In your state below.
Family and medical leave (FMLA)
The FMLA gives up to 12 weeks of unpaid, job-protected leave a year for:
The birth or adoption of a child.
Your own serious health condition.
Caring for a spouse, child or parent with a serious health condition.
You qualify only if your employer has 50 or more employees within 75 miles, and you have worked there 12 months and at least 1,250 hours in the last year. Your health insurance continues during the leave.
Some states run paid family leave programs that pay part of your wage. This differs by state.
Pregnancy and new parents
Employers with 15 or more workers must give reasonable changes for pregnancy, such as more breaks or a stool, under the Pregnant Workers Fairness Act.
Most workers have the right to break time and a private place (not a bathroom) to pump breast milk for one year after birth.
Check the company calendar or HR system for the rules.
Ask your manager early, in writing, especially for long trips home ("I would like to take PTO from June 3 to June 21").
Plan who will cover your work.
Booking flights before your manager approves the dates.
Taking long leave without checking your visa rules. Some work visas expect you to keep working; ask your attorney before unpaid leave.