Green Card

Once the 2-year period is over and it's time for the green card, what does the immigrant have to go through?

you mean, going from the UK to the US?
If so, wouldnt you be better off asking on Dive Into America or something?

Once the 2-year period is over and it's time for the green card, what does the immigrant have to go through?

Could you be a little more specific? Why would you wait two years for the green card?

Once the 2-year period is over and it's time for the green card, what does the immigrant have to go through?

You no longer have to wait 2 years/have ILR to apply for the GC from the Embassy in London. They have changed the requirement and it is 6 months residency in the UK of the US half of the relationship.

My friend told me that her and her husband had to go through a more extensive "proving" exercise after his initial 2-year card expired.  They moved from London to Boston.

If you are married for two years before you apply for the visa then you don't have any conditions to remove.

ETA:  Check out the http://www.visajourney.com for more info.