How does a deportee in Jamaica with a wife in the United States go about applying for reentry?

It will depend upon why the deportee was deported and when the deportation occurred. Some individuals who have been deported are not able to return while others may be able to return waivers. The first step would be to make sure you are eligible to return. The second step, assuming you can return, will be for your wife to file an immigrant visa on your behalf. You can read more about family immigration at http://myattorneyusa.com/family-immigration.