More countries are legislating presumed consent for organ donation, rather than explicit consent (e.g., your signature expressly confirming your wish to be an organ donor). A country with presumed consent would include every citizen on its organ-donation list, unless that person explicitly opts out. Some organ donors contribute organs while alive and healthy (e.g., a kidney), while others must first be declared dead, at which time organs or tissues are surgically removed. (Read more here.)
If you're wondering how a dead person can provide tissues or organs that are viable for a live recipient, here's the process: (1) A neurologist performs tests to determine brain death; (2) A medical team determines that the person can no longer breathe on his own. A dead brain and no breathing constitute official death. From OrganDonor.gov: Brain death is death and it is irreversible. Someone who is brain dead cannot recover. Only after brain death has been confirmed and the time of death noted, can organ donation become a possibility. (3) A computer search for matching recipients begins as a transplant surgical team replaces the original medical team. From OrganDonor.gov: Organs remain healthy only for a short time after removal, so minutes count. During the matching process and while transportation arrangements are made (by ambulance, helicopter, commercial plane) the donor organs are maintained on artificial support. Machines keep blood containing oxygen flowing to the organs. According to OrganDonor.gov, here's how long certain organs can remain viable outside the body: Heart and lungs: 4-6 hours, liver: 8-12 hours, pancreas: 12-18 hours, intestines: 8-16 hours, kidneys: 24-36 hours.