There are several ways of acquiring a second citizenship and the corresponding passport. These are birth, naturalization, marriage and investment.
Some countries allow non-resident individuals to obtain citizenship if their parents were born in that country. For example, Hungary allows persons not living in the country to obtain Hungarian citizenship provided they can show in the application that their parents are citizens.
Naturalization is the process by which a resident of a country can acquire citizenship, usually by residing in that country for a certain number of years as a permanent resident. For example, permanent residents of Canada must reside in Canada for four out of six years in order to be eligible to apply for citizenship. Persons with temporary status, such as students and foreign workers, must first gain permanent resident status in order to start counting their years as residents toward the citizenship requirement.
It is important to double check the requirements of your country of residence if you hope to acquire a second citizenship through naturalization.
Some countries grant fast-track permanent resident status to individuals who have married a citizen of that country, thereby speeding up the time to citizenship. For example, Canada allows spousal sponsorship, which results in automatic permanent resident status for the foreign spouse.
More and more countries are offering citizenship by investment programs or residency by investment programs to high net worth investors. Citizenship by investment is the process of acquiring a second citizenship by investing in the economy of the host country. Residency by investment programs offer permanent residency after the investment, which again speeds up the time to citizenship.