It is a total nightmare beyond total nightmares. I have British and Canadian citizenship, and am currently in the middle of the process of doing exactly as you suggested. They are so back logged that they are currently processing applications from August 2001. There are a number of different items for you to apply for. The following are the main forms you will need.
You will need to meet certain criteria in order to apply at all. You either need to have a relative (US citizen) that will sponsor you to come to the US, be married to a US citizen yourself, or have a job for a US company that is willing to sponser you. Lastly, if you can get into the country illegally, then you can apply for asylum.
Those are the only options of note. A good website for this is:
I am married to a US citizen, yet since coming to the US, I am not yet alllowed to work, and currently am not allowed to leave either, so it is pretty tough. The estimates to get a green card are another 60 days, I should be able to leave by May 1st, but getting residency will take about 3 years.
If you think of yourself as lucky, you can try the green card lottery that they run every year, it is free to apply (do not pay for this under any circumstances) but I do not think Canadians get much of an allocation.
Hope this helps