The fiancé visa is a several step process, and can become complicated very quickly.
Here are the steps (in a nutshell):
1) File a Fiancé Petition (I-129F) with US Citizenship and Immigration Services (USCIS). This petition needs to be accompanied by documents that prove that you've met in person in the last two years, documents that show that you have a bona fide relationship, and proof that you intend to get married with 90 days of your fiancé's arrival in the United States.
2) After the fiancé Petition is approved it is transferred to the National Visa Center (NVC), which will then forward your petition on to the consulate. During this time your fiancé should get his or her police certificate, gather proof that he or she is eligible to get married, and gather together the documents that he or she will need at the interview (birth certificate with translation, passport, etc.). When the consulate is ready they will send you a letter and then you'll submit the Non-immigrant visa online to the Department of State. Fiancé visas are considered non-immigrant since your fiancé will have to return home if you don't get married. Your fiancé will also need to get a medical examination and get any necessary vaccines. After the interview your fiancé will receive his or her passport with the visa attached to it within a week or so.
3) Fiancé travels to the US and you get married!
4) Once you are married your fiancé can apply for Adjustment of Status and get legal permanent residency (a green card) which enable him or her to travel in and out of the US and work in the US.
Things that may complicate the process are either party having a criminal record, trouble with immigration before (like a prior removal order), among other issues, so you should consult with an immigration attorney if you are interested in pursuing this process.