B-1/B-2 visa: your I-94 shows the date. Visitors are often given up to 6 months, but the officer can give less. Check your I-94 on the first day.
ESTA (Visa Waiver Program): up to 90 days. The I-94 class shows WT or WB. Short trips to Canada, Mexico or nearby islands do not restart the 90 days.
Tourism, visiting family, medical treatment, short business meetings, conferences, and short courses that are only for fun (not for credit).
Work, paid or unpaid, for a US company or person. This includes babysitting for a relative for money, cleaning, driving for Uber, or a "trial week" at a job.
Study for a degree or credits.
Treat the visit as moving here.
Remote work for your employer at home during a visit is a gray area. Keep it to normal business-visitor tasks and do not take US clients. If you plan to do more, ask an immigration attorney before you travel.
Need more time? (B visa only)
File Form I-539 with USCIS before your I-94 date passes. Online filing costs $420; paper costs $470 (current fee schedule).
Give a real reason (illness, a family event) and proof you can pay and will leave, such as a return ticket and bank statements.
You may stay while it is pending, but if it is denied you must leave right away.
ESTA visitors cannot extend or change status. In a real emergency, for example a hospital stay, CBP or USCIS may give up to 30 days of "satisfactory departure". Contact the Deferred Inspection office at once.
Your visa is canceled automatically, even for one day over. Next time you must apply in your home country.
An ESTA overstay means no more ESTA. You will need a visa.
More than 180 days over, then leaving: you cannot come back for 3 years.
One year or more over, then leaving: 10 years.
Counting 6 months from the visa date. Count from your I-94.
Doing small jobs "just to help". It can cost the visa.
Filing I-539 the day after the I-94 date. Late is almost always denied.