The first step of organ harvesting is to check the health condition of the organ. If the source is human, most countries require that the source is legally dead for organ transplantation purposes (e.g. cardiac or brain dead) or a voluntary healthy adult for the donation of some organs. Organs cannot be harvested after heart stops beating for a long time. Thus, a brain dead donor is preferred, but only a small percentage of deaths are brain deaths. Therefore, the majority of human organ sources are post cardiac death.
Donation after cardiac death involves surgeons to take organs within minutes of respirators and other forms of life support have being cut off from patients who still have at least some brain activity. DCD had been the norm for organ donors before 'brain death' became the standard in the early 1970s. Since then, most donors have been brain-dead. 
If consent is obtained from the source or the source's survivors, the next step is to perform a match between the source (donor) and the target (recipient) to reduce allergies. In the United States, the match between human donors and recipients is coordinated by groups like United Network for Organ Sharing. In the United Kingdom, the Human Tissue Authority did not yet rule on legality of donor matching web sites.
Co-ordination between teams working on different organs is often necessary in case of multiple-organ harvesting. Multiple-organ harvesting models are also developed from slaughtered pigs to reduce the use of laboratory animals
Quality of the organ then is certified. If the heart stopped beating for too long then the organ becomes unusable and cannot be used for transplant.
After organ harvesting the organs are often rushed to destination for emergency transplanting or preserved for later use or study.