Hi buddy, The process is easy but takes sometime.. I went through that back in 2005. You will just have to keep good relation with your current school and just find a good reason explaining to them why you want to change school. since you are probably on M1 VISA you will have to initiate a process for visa transfer from the one school to the other, So you have to ask your new school what papers they want from the old school and just then take copies etc from your current school and give them to the new one. The new school MUST KNOW of what papers are needed and they should know if they are professionals and authorized to issue VISAS. then you will have to do the tsa again in any case. and pay some fees for the visa transfer. not much.. i think around 150$.. the whole process might take you up to a month but not more... and always keep copies of everything for your records as they might be asked from you in the future if you come back in the usa for any reason.
Now if your current school does not want to cooperate or if you have argued with them then there is another way.. Just go back to your home country for a month and start a new process with your new school from there disregarding completely the old school... it is quite simple in that way ... if you choose that way be sure before leaving from the usa to make copies from your school file.. (visas papers etc) as they might be asked for at the us embassy at your country... good luck