So, you fall in love, but uh oh, your new love is "not from here". Whatever can you do. Try to not think of the movies "The Proposal" or "Greencard", as in many cases it is not that complicated, and of all the green card options out there, this is typically the easiest and fastest provided that you are actually married and living together etc. There are certainly some hoops to jump through and LOTS of paperwork, but quite straight forward for an experience immigration attorney.
You have several options once you are married. If your foreign spouse is already in the USA you can file an Adjustment of Status. If your fiance' is outside of the USA and you wish to marry in the USA, a K-1 fiance' visa would likely be the way to go. If you wish to marry abroad, you will need to file for permanent residency through consular processing. Note: Adjustment of Status is in my opinion the most straight forward, cheapest and least stressful way to go if you have it as an option.
A couple of misconceptions I often hear.
1) "When we get married, he automatically becomes a citizen" - FALSE Once you get married, in most cases your spouse will be entitled to Permanent Residency (Green Card).
2) "It doesn't matter how I came to America, if I marry a US citizen, I can get a Greencard" - FALSE If you didn't enter the country lawfully (undocumented), you are going to have some difficulty adjusting status.
3) If you enter on a Visa Waiver, you can get married and get a green card no problem. DEPENDS. This is a complicated question, as it brings in a concept of "Dual Intent". In essence, you can't enter the USA as a "Non-Immigrant" with the intent to become an "Immigrant". As it is an intent issue, it can often be overcome quite easily, but you need to be ready to prove that when you entered the country on a Visa Waiver or tourist visa that you did not intend to stay. As you may imagine, this could be tricky to prove if you got married one week after you entered the country on a visitors visa.
You can read more about this at www.uscis.gov