Almost all US jobs are at-will. That means:
Your employer can end your job at any time, for any legal reason or no reason, without notice.
You can quit at any time too. It is polite to give two weeks' notice.
It is still illegal to fire someone because of discrimination (race, religion, national origin, sex, age 40+, disability, pregnancy), or as retaliation for complaining about pay, safety or harassment. A written contract or a union agreement can also give you more protection.
A layoff means the company cuts jobs for business reasons, not because of you.
A federal law called WARN requires many employers with 100 or more workers to give 60 days' notice before large layoffs or plant closings.
Severance (extra pay when you leave) is not required by federal law. Many companies offer it if you sign a release (a promise not to sue). Read it carefully, ask for time, and ask if the amount can be increased.
If you lose your job: a checklist
Ask for your last day of work, your last day of pay, and when health insurance ends, all in writing.
Ask about your final paycheck and unused vacation. State law decides when it must be paid.
Health insurance: under COBRA, employers with 20 or more workers must let you keep the same plan for up to 18 months, but you pay the full cost plus up to 2%. Compare it with a plan at healthcare.gov; losing a job lets you sign up there within 60 days.
401(k): your money stays yours. Do not cash it out in a hurry; taxes and penalties can be high.
On a work visa? Your status clock may start right away. Read Laid off on H-1B or out of OPT days: the 60-day and 90-day rules and talk to an immigration attorney in the first week.
Unemployment insurance pays part of your old wage for some weeks while you look for work. Each state runs it.
Usually you must have lost the job through no fault of your own (such as a layoff), have worked and earned enough in the past year, and be able, available and looking for work.
You must be authorized to work during the weeks you claim. Green card holders and people with a valid work permit usually meet this. Many temporary visa holders do not, because their work permission ends with the job.
Apply in the first week after your job ends, on your state's unemployment website. Report your job search every week.
The amount, the number of weeks and the rules differ by state; see In your state below.
Signing a severance release on the same day without reading it.
Waiting to apply for unemployment. Benefits usually start from the date you apply, not the day you lost the job.