How to sponsor my same sex spouse to immigrate?
It has always been a piece of cake for a US citizen (the rules and wait times are somewhat different for permanent residents and holders of other types of immigrant and nonimmigrant visas in the United States but insofar as being able to let their spouse join them in the United States are concerned, going forward it would not matter whether you are married to a person of the same or different gender) to sponsor a foreigner (an alien as the lawyers like to call them) to join them and live legally in the country. Typically, the spouse gets a conditional green card to make sure that there is no marriage fraud, and after two years of being married (if the marriage ends before that, the alien is no longer eligible to be in the US), the condition is removed and the spouse gets a permanent resident status. If the alien wishes, after three years of being married, the spouse can file for naturalization and become a US citizen. If the couple divorces after two years, the spouse gets to keep the permanent resident status, but will need to wait 5 years to naturalize.
Spouse is already in the US legally: From now on, anyone in the United States who is eligible to sponsor a spouse to immigrate to the United States will be able to do so whether they are gays or lesbians. The process will be the same as it is for a heterosexual couple. For instance, if the spouse is already in the US legally, then, it simply means that you file USCIS Form I-130 to establish a marriage (it would, of course, be necessary that you first get married, if you are not legally married, and you can get married in any state that allows gay marriage in case you live in a state that has banned same-sex marriage; while you maybe ineligible for state benefits but as far as immigration is concerned you are all set) and at the same time USCIS Form I-485 to adjust status to permanent resident.
Spouse is overseas: You can file the paperwork to bring your fiance or spouse under the fiance visa so that the wait is very short. Then you do additional paperwork in the US to get a green card.
Spouse is in the US illegally at the time of filing: If the spouse entered the US legally, the paperwork is not much different than if the applicant were in the US legally, though, expect more scrutiny. However, the green card can be obtained without leaving the country. If the spouse entered the US illegally (basically by crossing the border illegally, or as the USCIS likes to call it EWI, entry without inspection), then, the spouse must go back to his or her native country to have an interview at the American consulate. Thankfully, due to the option to file USCIS Form I601A, the time spent overseas can be reduced to days/weeks and not months.