This really depends on your relationship with the other person and your status (e.g. US citizen, permanent resident, etc). Long story short, if you are the spouse or immediate family of an US citizen, there isn't any queue to get permanent resident status aside from whatever time it takes the US government to process the various forms. That time can be substantial, e.g. 2-3 years but it's nothing like the multi-year wait that a spouse of a permanent resident needs to go through just to apply for permanent resident status.