If you are not a citizen of the U.S. and you are about to marry a U.S. green card holder (someone with U.S. lawful permanent residence), you will not gain the right to work in the United States anytime soon. The entire application process, and thus the path to your gaining any meaningful rights in the U.S., is a lengthy one, because spouses of lawful permanent residents fall into a category known as "preference relatives."
People in the preference relatives category are subject to annual limits on the number of green cards given out, as well as per-country limits. They therefore face long waiting periods before they become eligible to apply for a green card and work permit, much less live and work in the United States. The wait is often four to five years long. If you want to see the original visa petition dates -- otherwise known as the "priority dates" -- of people who are just now receiving green cards, go the the State Department's Visa Bulletin and look on the family-based chart, under category F2A.
Only when a preference relative has risen to the top of the waiting list (has a current priority date) and has submitted an application for a green card will that person gain the right to both live and work in the United States. The exact timing and procedures depend on what country you are from and where you are living now and, if you're living in the U.S., whether you have the right "adjust status" here (that is, do the entire application process without leaving the country). Most spouses of permanent residents find they do not have the right to adjust status.
If you are living outside the U.S., then you must wait until your priority date becomes current to submit your application for a green card at a U.S. consulate. Only after that application has been processed will you be allowed to enter the U.S. as a permanent resident (green card holder).
Upon entry, you will be allowed all the rights of U.S. lawful permanent residents, including the right to work. However, your actual green card will be mailed to you a few weeks after your arrival. In the meantime, a stamp in your passport will serve as evidence of your permanent resident status.
If you're already in the U.S., your situation is complicated. We'll give a brief summary of the most likely scenarios below, but you should really see an immigration lawyer for a full analysis. As background, the most important thing to understand is that having an approved I-130 on file, and a priority date, gives you no rights to live or work here.
Find out whether you have any right to adjust status here. The answer is most likely no, unless you are grandfathered in under an old law known as Section 245(i). To be grandfathered in, someone would have had to have filed an approvable I-130 visa petition or a labor certification on your behalf before January 14, 1998; or done so before April 30, 2001, so long as you were also physically present in the U.S. on December 21, 2000.
By accruing unlawful presence in the U.S., you are making yourself inadmissible. The practical result of this is that, when your priority date becomes current and you travel to an overseas U.S. consulate to apply for your green card, you may be penalized for your unlawful U.S. stay with a time bar on your return. The bar is three years if you accrued unlawful presence of between 180 days and one year; or ten years if your unlawful presence lasted more than one year. (A waiver is available, but if it's denied, you're stuck outside the U.S.) There's also a so-called permanent bar for people who either lived in the U.S. unlawfully for a total of one year or more (in the aggregate, not necessarily continously) or were deported (removed), left the U.S., and then reentered or attempted to reenter illegally. (Actually, if subject to the permanent bar, you can request special permission to reapply for U.S. admission after ten years.)
You might want to consider leaving the U.S. now so as to protect your eventual right to a green card.
Again, because this is a long and drawn out process, marrying a U.S. lawful permanent resident is not a quick path to the right to work in the United States. Your U.S. resident fiance should look into filing for U.S. citizenship as soon as possible. When he or she becomes a citizen, you won't have to worry about waiting periods or priority dates anymore, but can immediately apply for a green card -- if, that is, you don't face problems due to an unlawful stay and inadmissibility. But if your latest entry to the U.S. was legal (with a visa) even this may not be a bar to adjusting status, based on your being the immediate relative of a U.S. citizen.
Yes, these laws are complex and confusing. Your best bet is to see an experienced immigration attorney for the details.