A Green Card is a document that authorizes a person to live and work in the USA.
Most immigrants have to fill in “an application for a green card”, Form I-485 (official name is Application to Register Permanent Residence or Adjust Status), to receive a green card and US permanent resident status.
A Green Card is usually issued for 10 years. In 5 years after receiving a green card you are eligible to apply for citizenship (naturalization) – Form N-400 (for spouses of US citizens the term is three years after receiving a green card).
If you do not want to receive citizenship, but to renew your green card you can do it having filed Form I-90. This form is also used to replace a stolen, damaged or lost green card or if there was a misprint in a present one (due to your or immigration service fault), or if you have changed your last name.
If you get married with a US citizen, you usually receive a conditional green card for 2 years. You can replace it for a permanent one in 2 years. Submit Form I-751 for it.