There are two simple ways for an immigrant to get into the country without brushing shoulders with the law. A US citizen will go to the immigration office and formally submit a petition for the non-citizen spouse and any children they may have. 

The process may be longer for marriages that are older than two years. According to USCIS, couples married for less than two years get IR1 visas. These are given shortly after the petition gets filed. 

You can obtain a US visa by petitioning for K-3. It gets offered in the country where the marriage took place. One must also have had a fiancée visa petition made on their behalf. It is the most common method for spouses to get a visa. 

Most immigrants who get married within the US have a high chance of getting their citizenship approved. One should prove that their marriage is real and not a sham to get through the immigration processes. 

According to the Bureau of Consular affairs, depending on their occupation, they will need to have proper certification or the organization they work with.  For artists, they must get recognition in the US. To get a labor certificate will require that the employer approves that they are going to work for them. Some petitions can only get petitioned several times a year. An interview is necessary only for people of certain ages. 

After a certain period, they can get a visa and citizenship as long as they do not break the law prior to and after entry into the country.