I'm 24, from Belfast (kind of Irish I guess!), CFI CFII, living in the US, and this is how I did it...
I came out to visit an American Girl & Family in 2000, that I had known for about 3 years -penpal, email, IM, etc. - for about 10 days prior to an interview with the Royal Marines. When I got back, I decided to cancel my interview, as I got cold feet about the career soldier thing, so I came back out for 3 months, on a Tourist Visa Waiver - this is only good for 90 days. During which I checked out a few local flight schools, picked one that could issue Student Visas (M-1) (although I really wanted to go to a different one that couldn't) and arranged for one to be issued for my return, to start flight training, I also started dating the Pen Friend.
M-1 was originally good for one year, but could be extended for another 12 months, if requested, while in the US. I requested an extension, and was told that it would take 350 days to determine whether I could stay for the year (basically another 15/16 days), meanwhile I was good to stay in the US while they made their minds up.
By this time I've been dating the same chick for almost 2 years, so I asked her parents if I could marry her. We made arrangements to have a quickie wedding in Las Vegas once my Visa ran out or if it was rejected, and a formal wedding for Family and Friends to attend - the proper wedding.
Once I received the letter of rejection from the INS, they gave me another 90 days to leave the country, during which we got married in Vegas, and started going through the necessary hoops to get me work authorization (very important), and a Green Card (to me not important). I had been working at the same place that issued my M-1 as a CFII, so it wasn't really illegal, but certainly fell into a grey area. I did my research online, and didn't hire an expensive lawyer / attorney as I felt it was only US government paperwork, and I knew that I would have an interview coming up soon, and a lawyer was a luxury I couldn't afford. I have heard that an attorney draws suspicion from the INS from someone whose lifestyle can't really afford one.
I got my Green Card issued in July 03, and I'm waiting until August to file a removal of conditional status. And I'm still happily married...
The moral of the story is to find ways to buy as much time as possible before marrying someone, be careful which state you live in, and or get married in (alimony - sometimes called vaginomony etc.) Or, just get married, in the first place as this will probably save a lot of hassle.