Get long-term visa or a residence permit in the United States. For this you will need a good reason, because a normal tourist visa for the move is not enough. If you have enough money, the easiest way is student visa. Enroll in a University in Miami, for example, Florida international University, and get marketable skills that will allow you later to work in the United States. If you already have marketable skills, find it in Miami of the employer and arrange with him for assistance in getting you a work visa. Miami is a major financial center of the American South, so people related to international Finance, will be easier to find a job there than other categories of professionals. Also, layaway can be a lottery green card. Each year the United States play a certain number of green card- permanent residence documentation among citizens of different countries, including Russia. To participate in the lottery you need to register on the official government website and wait for a response - you pay nothing, fee is charged only if you win.
Find housing in Miami. If you have the opportunity, buy tickets and come to the city in advance to personally to find accommodation. If you don't have time, find a temporary housing on the Internet. Please only local Agency Russian-language sites focused mainly on luxury housing, often at inflated prices. Do not rush to buy a house, even if you have enough money - first live in Miami and will definitely decide whether you want to stay in this town.
If you are moving with children, take care of their integration. In a good private school or kindergarten children need to write in advance. Also find out if the selected school adaptation classes for foreign children first, every schoolboy knows good English, can be difficult to understand the teacher and classmates.
Move your stuff from Russia to Miami. Please note that transportation will be quite expensive, so take only the most valuable things.