JC offered a very good list of alternatives. I recommend using the first alternative because it forces solvent through each component while atomized in the compressed air.
You will disconnect every component in order to flush it and IT IS VERY IMPORTANT to completely and thoroughly blow out the solvent before reassembly. At the time of reassembly, replace all orings and use the glandular sealant on them, which is a stringy grease sort of lubricant.
Also, if you want to really be thorough, find an auto air conditioning supply house and get a suction side filter, install this in the suction line just before entry to the compressor. This will catch any contaminants that you may miss before the reach and destroy your new compressor. If you install the suction side filter, you don't need to be as thorough with your flushing.
Also make sure you use a fresh filter-drier.