Temporary protected status (TPS) helps citizens of other countries to extend their stay in the United States if compelling, recognized reasons prevent them from returning to their own country.
You can't decide on your own that your country is unsafe and then apply for TPS. To be eligible, it's first necessary that the Secretary of U.S. Homeland Security designates your country for TPS. The Secretary may grant this designation if your country is in the midst of a war or other conflict, natural or environmental disaster, or similar situation that makes returning unsafe.
The country gets the TPS designation for a time period ranging between six and 18 months. Extensions are possible depending on the internal situation of the country so designated.
A person with TPS will not be asked to leave the United States, even if his or her permitted stay (most likely on a visa) has run out. TPS can also be used as a defense against removal, if you are in immigration court proceedings.
People granted TPS can also obtain a U.S. work permit. You'll receive a photo identity card called an Employment Authorization Document (EAD). You can also apply for a travel document (Advance Parole) allowing you to return to the U.S. after foreign travel.
However, TPS does not lead to permanent resident status (a green card). Moreover, a person with TPS will not be able to travel outside the United States and then return without first having received Advance Parole.
You won't be given TPS automatically. To apply for TPS, the primary form you need to fill in is USCIS Form I-821. In addition, you'll need to fill out Form I-765 for a work permit (even if you don't plan to work). If you think you'll want to travel, also prepare Form I-131.
You also need to pay a filing fee and submit certain documents. If you are 14 years of age or older, you need to pay a fee for biometric services (such as fingerprinting) as well.
All of these forms, plus information on filing fees and where to mail them, can be found on the USCIS website's TPS section.
There's more to establishing your eligibility for TPS than showing you're from the right country. You'll also need to prove that you've been continuously physically present in the U.S. since the date your country was most recently designated for TPS. And you'll be denied if USCIS finds that you've committed certain crimes (as will be shown from the fingerprint check that they'll run on you), persecuted others, or otherwise been disqualified.
You need to provide proof of your identity, nationality, and continual physical presence in the United States. Send copies (not originals) of documents such as your passport, birth certificate, hotel bills or apartments leases, pay stubs, medical records from U.S. doctors or hospitals, other bills and communications addressed to you within the United States, and so forth.
If the TPS for your country is extended, then you need to apply for TPS by filling in Forms I-821 and I-765 again. This time around there is no fee for the I-821, only for the work permit form, I-765. And you won't need to provide all the supporting documents this time around.