Every there are thousands of people who immigrate to the United States and many more who want to but are not able to. In order to have any chance of success at being able to immigrate it is important that you be able follow the procedures properly. These will vary slightly for some people but the general procedure for most people is the same.
The first step in immigrating to the United States for most people is to have somebody file a petition on your behalf. This is not something that you can do yourself you need to have a sponsor do it for you. If you are immigrating on the grounds that you have been offered a job your employer will have to do it, if you are coming because you have family then the family member will have to make the petition. There are some exceptions to this like asylum seekers (contact Joe Kakaletris for more info about this procedure!) but for most people this is how the process gets started.
The next step after your petition has been approved is that you will need to fill out a visa application. This has to be done in your home country through either the US Embassy or Consulate. Again there are exceptions to this like refugees but most people will have to do it this way. There is a lot of information required on your visa application so make sure that you are ready to provide it, mistakes or missing information will really delay the process.
Once your application has been filled out you will be invited to an interview to determine your suitability. This will most involve them verifying the information on your application so you will need to have the documentation to back up whatever you put on there. The required documentation will vary depending on which type of visa you are applying for. The interview will also be used to determine your suitability to immigrate to the US. During the interview you will be finger printed, refusal to agree to this will result in your application being rejected.
After you have been issued your visa you will be allowed to enter the United States. After doing this you will need to fill out an application for a green card if you are planning to become a permanent resident. This is an important step since if you don't do it you are likely to be deported. There are of course exceptions to the above procedures but this is how the vast majority of people would do it. After you get your green card and have lived in the US for a specified period of time you will be allowed to apply for citizenship. This is a fairly involved process so you will need to look up all of the details that are involved.