A US citizen or a green card holder can file a petition with immigration service for his/her relatives (spouses, children, parents, brothers and sisters) to migrate to the USA. It is called family reunification and the first step is to file Form I-130.
You will have to wait for your turn to receive a green card through family, as there are quotes for most of the categories (exception: spouses and parents of US citizens).
Having received an immigration visa, relatives enter the USA and receive their green cards by mail within two weeks.
Processing time depends on your status (a green card holder or U.S. citizen) and who you want to reunite with. Brothers and sisters of U.S. citizens wait for the longest time (now it takes about 10 years). The procedure takes about one year for US spouses.
For political refugees
You can reunite with your spouse or children under 21 within 2 years since you have obtained refugee status providing that you have included them into your asylum application (Form I-589).
Complete Form I-730 to reunite with your family.